A General Multitype Branching Process with Age, Memory and Population Dependence Christine Jacob

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A general multitype branching process with age, memory and population dependence Christine Jacob

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Christine Jacob. A general multitype branching process with age, memory and population dependence. IWAP 2010 V-th. International Workshop on Applied Probability, Jul 2010, Madrid, Spain. hal- 02755517

HAL Id: hal-02755517 https://hal.inrae.fr/hal-02755517 Submitted on 3 Jun 2020

HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. IWAP 2010 5th International Workshop on Applied Probability

BOOK OF ABSTRACTS AND DETAILED PROGRAMME

5-8 July, 2010 Colmenarejo, Madrid, Spain

Universidad Carlos III de Madrid, Spain

Preface

The 5th International Workshop in Applied Probability, IWAP 2010, held in Colmenarejo, Madrid, Spain, has been built on the success of previous meetings. These meetings took place at Sim´onBol´ıvar Univer- sity (Venezuela, 2002), University of Piraeus (Greece, 2004), University of Connecticut (USA, 2006) and University of Technology of Compi`egne(France, 2008). Over 300 researchers in applied probability from all over the world are attending this workshop, making IWAP 2010 one of the largest IWAPs.

Currently, IWAP is one of the major international meetings for researchers in Applied Probability. IWAP 2010 covers a wide range of research areas in stochastic processes, statistic and probability; featuring seven invited plenary lectures presented by leading specialists, a large variety of invited sessions, oral contributions, and posters. The conference is co-sponsored by Bernoulli Society and Institute of Mathematical Statistics and supported by Universidad Carlos III de Madrid.

The aim of this workshop is to bring together and foster collaboration among scientists engaged in the ﬁeld, which is becoming more and more important in many real life problems. Many papers presented at the IWAP 2010 concern important topics, having applications in diﬀerent areas of science and technology.

The current volume is divided in two main parts:

1. Detailed programme

2. Book of abstracts

We hope you enjoy this information and this meeting.

Joseph Glaz and Juan Romo

iii Sponsors

• Bernoulli - Society for Mathematical Statistics and Probability

• Institute of Mathematical Statistics

• Universidad Carlos III de Madrid

iv Workshop Chairs:

Joseph Glaz, University of Connecticut, USA. Juerg Huesler, University of Bern, Switzerland. Markos Koutras, University of Piraeus, Greece. Nikolaos Limnios, Universite Technologie de Compiegne, France. Jose Louis Palacios, Universidad Sim´onBol´ıvar, Venezuela. Juan Romo, Universidad Carlos III de Madrid, Spain.

Organizing Committee:

AndrésAlonso Ana Arribas Héctor Cañada Ignacio Cascos Mar´ıaDurbán Alba Franco Raul Jiménez Rosa Lillo Elisa Molanes Rosario Romera Juan Romo (Chair) Nuria Torrado Universidad Carlos III de Madrid, Spain.

Scientiﬁc Committee:

Vladimir Anisimov, GlaxoSmithKline, Essex, UK. Kostya Borovkov, University of Melbourne, Australia. Ghislaine Gayraud, University of Technology of Compiegne, France. Vladimir Koroliuk, Ukrainian National Academy of Science, Ukraine. Dirk Kroese, University of Queensland, Australia. Claude Lefevre, UniversitéLibre de Bruxelles, Belgium. Nancy Lopes Garc´ıa, University of Campinas, Brazil. Gábor Lugosi, Universidad Pompeu Fabra, Spain. Hosam Mahmoud, George Washington University, USA. Raimondo Manca, University of Rome La Sapienza, Italy. David Perry, University of Haifa, Israel. Marco Scarsini, LUISS, Italy. Moshe Shaked, University of Arizona, USA. Christos H. Skiadas, Technical University of Crete, Greece. Dmitrii Silvestrov, Stockholm University, Sweden. Philippe Vieu, Institut de Mathématiquesde Toulouse, France. Joseph E. Yukich, Lehigh University, USA.

Contents

Programme Table ...... 1

Detailed Programme ...... 3

Monday...... 3

Tuesday ...... 12

Wednesday ...... 17

Thursday ...... 25

Abstracts ...... 29

Plenary Talks ...... 31

Invited Talks ...... 35

Contributed Talks ...... 97

Posters ...... 137

Authors Index ...... 143

vii

Programme Table

Monday Tuesday Wednesday Thursday 09:15 - 09:30 Opening

09:30 - 10:15 Plenary I Plenary III Plenary V Plenary VII

10:15 - 10:45 Long coffee break Long coffee break Long coffee break Long coffee break

10:45 - 12:15 Invited Sessions I Invited Sessions III Invited Sessions V Invited Sessions VII

12:15 - 12:30 Break Break Break Break

12:30 - 14:00 Invited Sessions II Invited Sessions IV Invited Sessions VI Invited Sessions VIII

14:00 - 15:15 Lunch Lunch Lunch Lunch

Contributed Contributed 15:15 - 16:15 Plenary IV Sessions I & announcements Sessions III

16:15 - 16:30 Coffee break Visit to San Coffee break Lorenzo del Escorial and Contributed Contributed 16:30 - 17:30 Cocktail Sessions II Sessions IV

17:30 - 17:45 Break Break

17:45 - 18:30 Plenary II Plenary VI

Special Poster 18:45 - 19:30 Session

Schedule Poster Session according to (cont.) and Tapas Gala Dinner the actiivity table

Detailed Programme

Monday, July 5th, 2010

9:15 - 9:30 Opening Auditorio Daniel Pe˜na- President of Universidad Carlos III de Madrid 9:30 - 10:15 Plenary Talk: Paul Embrechts Auditorio Model uncertainty in ﬁnancial risk management

10:15 - 10:45 Long coﬀee break

10:45 - 12:15 Invited Session I-I: Statistical Model-Testing Room 1.0.B02 Organizers: JoséR. Berrendero & Javier Cárcamo 10:45 - 11:15 Trimming methods in model validation Pedro César Alvarez´ Esteban 11:15 - 11:45 Multivariate uniformity tests for the case of unknown support JoséR. Berrendero 11:45 - 12:15 Linear discrimination under heteroscedasticity Javier Cárcamo ...... 10:45 - 12:15 Invited Session I-II: Semi-Markov Chains and Hidden Models Room 1.0.B03 Organizers: Vlad Barbu & Nikolaos Limnios 10:45 - 11:15 Large deviations and their applications to the problem of exit from a domain Adina Oprisan 11:15 - 11:45 Testing hypotheses for semi-Markov processes Vlad Barbu 11:45 - 12:15 A hidden seasonal switching model for high resolution breakpoint rainfall data Peter Thomson ...... 10:45 - 12:15 Invited Session I-III: Stochastic Geometry and Stereology Room 1.0.B04 Organizer: Viktor Benes 10:45 - 11:15 Flowers and wedges as new tools for the stereology of particles Luis Cruz-Orive 11:15 - 11:45 CLTs for Poisson hyperplane processes and extremal problems for convex bodies Lothar Heinrich

3 11:45 - 12:15 Moment estimation for inhomogeneous spatial Cox processes Michaela Prokesova ...... 10:45 - 12:15 Invited Session I-IV: Issues in Actuarial Sciences and Risk Theory Room 1.0.B05 Organizer: Esther Frostig 10:45 - 11:15 Optimal insurance with counterparty default risk Enrico Biffis 11:15 - 11:45 Finite time ruin probabilities for phase-type claims Konstadinos Politis 11:45 - 12:15 Asymptotic analysis of a risk process with high dividend barrier Esther Frostig ...... 10:45 - 12:15 Invited Session I-V: Particle Systems Room 1.0.B06 Organizer: Pablo Ferrari 10:45 - 11:15 A stochastic model of evolution Fábio Machado 11:15 - 11:45 The crossover to the KPZ equation Ana Patricia Gon¸calves 11:45 - 12:15 Kinetically constrained models: non-equilibrium coarsening dynamics Cristina Toninelli ...... 10:45 - 12:15 Invited Session I-VI: Spatial Models Room 1.0.B07 Organizer: Wenceslao GonzálezManteiga 10:45 - 11:15 Bivariate splines for spatial functional regression and forecasting Serge Guillas 11:15 - 11:45 A coherence-based measure for spatial classification Jorge Mateu 11:45 - 12:15 Cross-covariance functions for multivariate random fields based on latent dimensions Marc Genton ...... 10:45 - 12:15 Invited Session I-VII: Application of Stochastic Control Room 1.0.B08 Organizer: Wolfgang J. Runggaldier 10:45 - 11:15 Controlled diffusion processes and full cooperation in environmental topics Wojciech Szatzschneider 11:15 - 11:45 Stochastic iterative dynamic programming applied to optimal control problems Héctor Cañada-Jaime 11:45 - 12:15 On optimal investment in a reinsurance context with a point process market model Wolfgang Runggaldier ...... 10:45 - 12:15 Invited Session I-VIII: Sequential Analysis Editor’s Session Room 1.0.B09 Organizer: Nitis Mukhopadhyay

4 10:45 - 11:00 Announcement of the winner(s) of Abraham Wald Prize in Sequential Anal- ysis 11:00 - 11:30 Two-stage inference methods for “large p, small n” scenarios: Part I Kazuyoshi Yata 11:30 - 12:00 Two-stage inference methods for “large p, small n” scenarios: Part II Makoto Aoshima 12:00 - 12:15 Q & A

12:15 - 12:30 Break

12:30 - 14:00 Invited Session II-I: Model Assessment Room 1.0.B02 Organizer: Alejandra Cabaña 12:30 - 13:00 The drunken man and goodness-of-fit Michael Stephens 13:00 - 13:30 Assessing ARMA models for stationary time series by transforming accumulated residues processes Enrique M. Cabaña 13:30 - 14:00 CLT for multiple integrals with respect to the empirical process. Applications to the Wasserstein test HélèneBoistard ...... 12:30 - 14:00 Invited Session II-II: Statistical Seismology Room 1.0.B03 Organizers: Georgios Tsaklidis & Nikolaos Limnios 12:30 - 13:00 Forecasting macroseismic scenarios through anisotropic attenuation: A Bayesian approach Renata Rotondi 13:00 - 13:30 Bayesian estimation of doubly stochastic Poisson processes for detection of seismicity phases Elisa Varini 13:30 - 14:00 Itôequation out of domino cellular automaton Zbigniew Czechowski ...... 12:30 - 14:00 Invited Session II-III: Set Estimation Room 1.0.B04 Organizer: Antonio Cuevas 12:30 - 13:00 Set and set properties estimation Gérard Biau 13:00 - 13:30 On uniform consistency in set estimation Antonio Cuevas

5 13:30 - 14:00 Computational methods and algorithms in set estimation Beatriz Pateiro-López ...... 12:30 - 14:00 Invited Session II-IV: Probability and Actuarial Sciences Room 1.0.B05 Organizer: StéphaneLoisel 12:30 - 13:00 Asymptotic finite-time ruin probabilities for a class of path-dependent claim amounts using Poisson spacings Romain Biard 13:00 - 13:30 Ruin-probabilistic estimation of operational risk capital in finance and insurance Vladimir Kaishev 13:30 - 14:00 Ultimate ruin probability in discrete time with Bühlmanncredibility premium adjustments Julien Trufin ...... 12:30 - 14:00 Invited Session II-V: Branching Processes Room 1.0.B06 Organizers: Miguel González& InésM. del Puerto 12:30 - 13:00 Stochastic and deterministic population processes: From branching to the transport equation Marek Kimmel 13:00 - 13:30 A general multitype branching process with age, memory and population dependence Christine Jacob 13:30 - 14:00 Statistical inference for controlled multitype branching processes InésM. del Puerto ...... 12:30 - 14:00 Invited Session II-VI: Inference on Stochastic Models Room 1.0.B07 Organizer: Miguel López 12:30 - 13:00 Composite likelihood-based estimation methods for space-time stochastic processes Jorge Mateu 13:00 - 13:30 Assessing the impact of autocorrelation in misleading signals in simultaneous residual schemes for the process mean and variance: numerical and stochastic ordering approaches AntónioPacheco 13:30 - 14:00 Ranking shape variability Miguel López ...... 12:30 - 14:00 Invited Session II-VII: Stochastic Control Room 1.0.B08 Organizer: Onésimo Hernández-Lerma 12:30 - 13:00 Semi-Markov control processes with partially known holding times distribution Fernandeo Luque-Vásquez 13:00 - 13:30 Undiscounted optimality criteria in economics and finance Marco A. Méndez-Salazar

6 13:30 - 14:00 Constrained control of continuous-time Markov chains Tom´asPrieto-Rumeau ...... 12:30 - 14:00 Invited Session II-VIII: Multi-Stage and Sequential Methodologies Room 1.0.B09 Organizer: Tumulesh K. S. Solanky 12:30 - 13:00 On Bayesian analysis in multistage designs Pierre Bunouf 13:00 - 13:30 Two-stage and sequential estimators of the normal variance Shelemyahu Zacks 13:30 - 14:00 On two-stage comparisons with a control under heteroscedastic normal distributions Nitis Mukhopadhyay

14:00 - 15:15 Lunch

15:15 - 16:15 Contributed Session I-I: Central Limit Theorems and Large Deviations Room 1.0.B02 15:15 - 15:35 A central limit theorem and its applications to multicolor randomly reinforced urns Irene Crimaldi 15:35 - 15:55 Central limit theorem for the number of near-records F. Javier L´opez 15:55 - 16:15 Large deviation inequalities for N-demimartingales and negatively associated random variables Milto Hadjikyriakou ...... 15:15 - 16:15 Contributed Session I-II: Branching Processes Room 1.0.B03 15:15 - 15:35 Branching walks in inhomogeneous environments and their applications in the theory of epidemics Elena Yarovaya 15:35 - 15:55 Population, catastrophes and extinction probability: analytical bounds for the extinction criteria Giang Nguyen 15:55 - 16:15 Populations, catastrophes and extinction probability: Algorithmic methods Sophie Hautphenne ...... 15:15 - 16:15 Contributed Session I-III: Semiparametric and Nonparametric Estimation Room 1.0.B04 15:15 - 15:35 Robust methods in semiparametric estimation with missing responses Graciela Boente

7 15:35 - 15:55 Kernel estimators of density functionals with reduced bias JoséE. Chacón 15:55 - 16:15 A semi-parametric approach for time-to-event forecasting Alejandro Veen ...... 15:15 - 16:15 Contributed Session I-IV: Bayesian methods and applications Room 1.0.B05 15:15 - 15:35 Age and disability in Spain: An estimation using non-linear methods Pablo Alonso González 15:35 - 15:55 Mixture modeling and convex ordering for bio-inspired communication, rooted network and maintenance Eva Mar´ıaOrtega 15:55 - 16:15 Modelling ozone pollution in Mexico city Juan M. Barrios ...... 15:15 - 16:15 Contributed Session I-V: Risk Models I Room 1.0.B06 15:15 - 15:35 Semi-Markov risk migration models with initial and final backward: A case study Giuseppe Di Biase 15:35 - 15:55 An insurance risk model with Parisian implementation delays Jean-Fran¸coisRenaud ...... 15:15 - 16:15 Contributed Session I-VI: Applications to Physics and Engineering Room 1.0.B07 15:15 - 15:35 Extended dependency tree-HMM non-rectangular sub-image modeling Mohamed El Yazid Boudaren 15:35 - 15:55 Statistical characterization of the time-delay for web-based networked telerobots Ana Gago-Ben´ıtez 15:55 - 16:15 Generalized scale invariance in finite range systems Sandra Chapman ...... 15:15 - 16:15 Contributed Session I-VII: Diffusion Processes Room 1.0.B08 15:15 - 15:35 On the crossing times of a one-dimensional diffusion process through two boundaries Cristina Zucca 15:35 - 15:55 On the first passage time for bivariate diffusion processes Laura Sacerdote 15:55 - 16:15 On boundary crossing probabilities for diffusion processes Konstantin Borovkov

16:15 - 16:30 Coﬀee break

8 16:30 - 17:30 Contributed Session II-I: Particle Systems and Related Fields Room 1.0.B02 16:30 - 16:50 An urn-based spatio-temporal shock model for cancer growth modeling Pasquale Cirillo 16:50 - 17:10 From micro to macro description of a system of stochastic particles subject to nonlocal interactions Vincenzo Capasso 17:10 - 17:30 Asymptotic behavior of a system of stochastic particles subject to nonlocal interactions Daniela Morale ...... 16:30 - 17:30 Contributed Session II-II: Dynamic and Stochastic Resource Allocation Prob- lems Room 1.0.B03 16:30 - 16:50 Benchmarking restless bandit index policies in a multitarget tracking model Sof´ıaSoledad Villar 16:50 -17:10 On the multi-armed bandit problem and its Lagrangian relaxation Peter Jacko 17:10 - 17:30 Optimal policies under full history dependence: Robbins’ problem Yvik Swan ...... 16:30 - 17:30 Contributed Session II-III: Stochastic Geometry and Point Processes Room 1.0.B04 16:30 - 16:50 Stabilization and limit theory for random polytopes Tomasz Schreiber 16:50 - 17:10 On point processes and random marked sets Viktor Benes 17:10 - 17:30 Covering the whole space with Poisson random balls Anne Estrade ...... 16:30 - 17:30 Contributed Session II-IV: Statistical Models for Natural Phenomena Room 1.0.B05 16:30 - 16:50 A spatio-temporal Poisson model to estimate the density of blue whales in the Antartide Mar´ıaCruz Valsero Blanco 16:50 - 17:10 Estimation of the expected number of earthquake occurrences based on semi-Markov models Irene Votsi 17:10 - 17:30 Predicting residential losses in Florida by the public model Sneh Gulati ......

9 16:30 - 17:30 Contributed Session II-V: CLT’s for Stochastic Processes Room 1.0.B06 16:30 - 16:50 Central limit theorem and p-variations Hermine Biermé 16:50 - 17:10 Multipower variation for Brownian semistationary processes JoséManuel Corcuera 17:10 - 17:30 Limit theorems for stationary Markov additive processes James Ledoux ...... 16:30 - 17:30 Contributed Session II-VI: Queues Room 1.0.B7 16:30 - 16:50 Fairness and efficiency in waiting times for polling models with the k-gated service discipline Sandra (A.C.C.) van Wijk 16:50 - 17:10 Queueing analysis of error-prone production systems Dieter Fiems 17:10 - 17:30 Finite two-queue systems where customers of each queue are the servers of the other queue Uri Yechiali ...... 16:30 - 17:30 Contributed Session II-VII: Probability Distribution Theory Room 1.0.B08 16:30 - 16:50 Some classification results of generalized mixtures of Weibull distributions Manuel Franco 16:50 - 17:10 An asymptotic expansion for the tail of compound sums of Burr distributed random variables Dominik Kortschak ...... 16:30 - 17:30 Contributed Session II-VIII: Complex Data Analysis Room 1.0.B08 16:30 - 16:50 Partially sequential Lepage-Wolfe type test for a location-scale problem in environmental monitoring Amitava Mukherjee 16:50 - 17:10 Application of overrepresentation for estimating results of tracking surveys Wieslawa Dabala 17:10 - 17:30 Hemachandra numbers, indian music, and patterns in coin tossing M. B. Rao

17:30 - 17:45 Break

10 17:45 - 18:30 Plenary Talk: Ricardo Fraiman Auditorio Estimating boundary measures of general sets

18:45 - 19:30 Special Poster Session Hall P1 Clustering integer-valued time series AndrésM. Alonso P2 Regions of controlled posterior risk Sandra Mar´ıaBargãoSaraiva Ferreira P3 A relation between the distributions of stopping time and stopped sum via Wald’s identity Michael Boutsikas P4 Modeling rare events through a pRARMAX process Marta Ferreira P5 Chains of infinite memory: what can we say without assuming continuity Alexsandro Gallo P6 Classification of genomic sequences via wavelet variance and a self-organizing map with an application to mitochondrial DNA Agnieszka Jach P7 Multiscale entropy-based analysis of the effect of deformation on intermittency Ana-Esther Madrid P8 Limit theorems for a rumour process with random stifling Pablo Mart´ın-Rodr´ıguez P9 Risk measures and stochastic orderings using the Lorenz curve Miguel Mendes P10 Modelling extremal dependence in stock indices Alexandra Ramos P11 Goodness-of-fit test for density estimation with directional data Daniela Rodr´ıguez P12 Robust inference in generalized linear models Isabel Rodrigues P13 Testing fit for grouped circular data Zheng Sun P14 Poisson approximation of the mixed Poisson distribution with infinitely divisible mixing law Effie Vaggelatou

11 Tuesday, July 6th, 2010

9:30 - 10:15 Plenary Talk: Montserrat Fuentes Auditorio Spatial bayesian quantile regression: Application to study the impact of climate change on tropospheric ozone

10:15 - 10:45 Long coﬀee break

10:45 - 12:15 Invited Session III-I: Extremes and Risks Room 1.0.B02 Organizer: Mar´ıaIvette Gomes 10:45 - 11:15 Tail behaviour of β-ARCH processes Laszlo Markus 11:15 - 11:45 Pseudo-empirical likelihood inference for clusters of rare events Christian-Yann Robert 11:45 - 12:15 Semi-parametric probability-weighted moments estimation revisited Mar´ıaIvette Gomes ...... 10:45 - 12:15 Invited Session III-II: Stochastic 3D Modelling of Morphological Microstruc- tures Room 1.0.B03 Organizer: Volker Schmidt 10:45 - 11:15 Modeling fiber reinforced polymers Hellen Altendorf 11:15 - 11:45 Modelling the microstructure of foams using random tessellations Claudia Redenbach 11:45 - 12:15 Random geometric graphs for modelling the pore system of fibre-based materials Ralf Thiedmann ...... 10:45 - 12:15 Invited Session III-III: Sequential Detection and Estimation I Room 1.0.B04 Organizers: George Moustakides, Alex Tartakovsky & Igor Nikiforov 10:45 - 11:15 Sequential detection of change-points in state-space models Boris Brodsky 11:15 - 11:45 Wiener disorder problem with observations at fixed discrete time epochs Savas Dayanik 11:45 - 12:15 Epidemic detection using CUSUM Georgios Fellouris ...... 10:45 - 12:15 Invited Session III-IV: Heavy Traffic Limits Room 1.0.B05 Organizer: David Perry

12 10:45 - 11:15 Heavy-traffic limits via an averaging principle; convergence and stability Ohad Perry 11:15 - 11:45 Blind fair routing in large-scale service systems Amy Ward 11:45 - 12:15 On optimality gaps of asymptotically optimal policies in many-servers heavy-traffic Itai Gurvich ...... 10:45 - 12:15 Invited Session III-V: Stochastic Orders Room 1.0.B06 Organizer: Moshe Shaked 10:45 - 11:15 Stochastic ordering comparisons of sampling designs Yosef Rinott 11:15 - 11:45 Weighted sums, stochastic orders, and entropy Yaming Yu 11:45 - 12:15 Stochastic orders in network security Xiaohu Li ...... 10:45 - 12:15 Invited Session III-VI: Cloning and Splitting for Rare Event Simulation and Counting Room 1.0.B07 Organizer: FrédéricCérou 10:45 - 11:15 Stochastic enumeration method for rare-events, counting and combinatorial optimization Reuven Rubinstein 11:15 - 11:45 Iterative Monte Carlo for extreme quantiles and extreme probabilities Arnaud Guyader 11:45 - 12:15 Rare event simulation for a static distribution FrédéricCérou ...... 10:45 - 12:15 Invited Session III-VII: Probability and Statistics for Genomics Room 1.0.B08 Organizers: Stéphane Robin & Sophie Schbath 10:45 - 11:15 Moderate deviations for word counts in biological sequences Sarah Behrens 11:15 - 11:45 Distributions of statistics over factor graphs Donald E. K. Martin 11:45 - 12:15 Exact posterior distributions over the segmentation space and model selection for multiple change-point detection problems StéphaneRobin ...... 10:45 - 12:15 Invited Session III-VIII: Economic Applications Room 1.0.B09 Organizer: Marco Scarsini 10:45 - 11:15 Expectiles as risk measures Alfred Müller

13 11:15 - 11:45 Pareto eﬃciency for the concave order and multivariate comonotonicity Guillaume Carlier 11:45 - 12:15 Fear of loss, inframodularity, and transfers Marco Scarsini

12:15 - 12:30 Break

12:30 - 14:00 Invited Session IV-I: Insurance Risk Theory Room 1.0.B02 Organizer: Claude Lefèvre 12:30 - 13:00 Reinsurance and solvency M. MercèClaramunt 13:00 - 13:30 Actuarial applications of epidemiological models JoséGarrido 13:30 - 14:00 Stochastic modelling of portfolio experienced mortality: A co-integration based approach StéphaneLoisel ...... 12:30 - 14:00 Invited Session IV-II: Stochastic Geometry Room 1.0.B03 Organizer: Tomasz Schreiber 12:30 - 13:00 Visibility estimates in the Boolean model Pierre Calka 13:00 - 13:30 Estimating surface integrals on the boundary of unknown bodies: An application to Google Earth RaúlJiménez 13:30 - 14:00 Moment analysis of the Delaunay tessellation field estimator Marie-Colette van Lieshout ...... 12:30 - 14:00 Invited Session IV-III: Sequential Detection and Estimation II Room 1.0.B04 Organizers: George Moustakides, Alex Tartakovsky & Igor Nikiforov 12:30 - 13:00 On-line change detection and condition-based maintenance for a non-homogenous Gamma process Mitra Fouladirad 13:00 - 13:30 Multi-dimensional quickest detection in coupled stochastic network Olympia Hadjiliadis 13:30 - 14:00 Sequential decision procedures in networks Igor Nikiforov ...... 12:30 - 14:00 Invited Session IV-IV: Asymptotics in Queueing Networks Room 1.0.B05 Organizer: David Perry

14 12:30 - 13:00 Asymptotically optimal dynamic pricing for network revenue management Rami Atar 13:00 - 13:30 A Lévyinput model with state-dependent services Maria Vlasiou 13:30 - 14:00 Scaling limits for bandwidth sharing networks Bert Zwart ...... 12:30 - 14:00 Invited Session IV-V: Stochastic Orders: General Theory Room 1.0.B06 Organizer: Moshe Shaked 12:30 - 13:00 Multivariate dispersion for random vectors having a common copula Alfonso Suárez-Llorens 13:00 - 13:30 Multivariate likelihood ratio ordering of ordered data FélixBelzunce 13:30 - 14:00 Recent development of ordering conditional ordered data Baha-Eldin Khaledi ...... 12:30 - 14:00 Invited Session IV-VI: MCMC Methodology and Theory Room 1.0.B07 Organizer: Gareth Roberts 12:30 - 13:00 Riemannian Manifold Hamiltonian Monte Carlo and population MCMC methods for estimating Bayes Factors Ben Calderhead 13:00 - 13:30 Hybrid Monte-Carlo in high dimensions Alexandros Beskos 13:30 - 14:00 Geometric ergodicity and the spectral gap of non-reversible Markov chains Ioannis Kontoyiannis ...... 12:30 - 14:00 Invited Session IV-VII: Applied Probability in Genomics Room 1.0.B08 Organizer: Catherine Matias 12:30 - 13:00 Local motif detection in biological networks based on Poisson approximation Etienne Birmelé 13:00 - 13:30 Inference for context-dependent nucleotide substitution models Jean Bérard 13:30 - 14:00 Parameter estimation in multiple hidden i.i.d. models from biological multiple alignment Ana Arribas Gil ...... 12:30 - 14:00 Invited Session IV-VIII: Semi-Markov Actuarial Models Room 1.0.B09 Organizer: Raimondo Manca 12:30 - 13:00 Stock valuation along a semi-Markov chain Guglielmo D’Amico

15 13:00 - 13:30 A Monte-Carlo semi-Markov backward model for a distributional claim reserve construction Raimondo Manca 13:30 - 14:00 A parametric semi-Markov model for the study of the mortality evolution Filippo Petroni

14:00 - 15:15 Lunch

15:15 - 16:00 Plenary Talk: Victor de la Pe˜na Auditorio A method for estimating threshold crossing time with application to climate change

16 Wednesday, July 7th, 2010

9:30 - 10:15 Plenary Talk: Robin Pemantle Auditorio Probability and the analysis of algorithms: examples and open problems

10:15 - 10:45 Long coﬀee break

10:45 - 12:15 Invited Session V-I: Stochastic Orders: Applications in Reliability and Finance Room 1.0.B02 Organizer: Félix Belzunce 10:45 - 11:15 New ordering results for coherent system lifetimes Jorge Navarro 11:15 - 11:45 On the consistency of distorted variability measures with respect to dispersive orders Miguel Angel´ Sordo 11:45 - 12:15 Stochastic comparisons of multivariate mixtures Moshe Shaked ...... 10:45 - 12:15 Invited Session V-II: Sequential Detection and Estimation III Room 1.0.B03 Organizers: George Moustakides, Igor Nikiforov & Alex Tartakovsky 10:45 - 11:15 Quickest sequential opportunity search in multichannel systems Lifeng Lai 11:15 - 11:45 Minimax optimality of the Shiryaev-Roberts procedure Alexander Tartakovsky 11:45 - 12:15 Bayesian quickest transient change detection Venugopal Veeravalli ...... 10:45 - 12:15 Invited Session V-III: Probability Tools in Selection and Validation of Models Room 1.0.B04 Organizer: Carlos Matrán 10:45 - 11:15 Asymptotics for model checking methods based on trimming Eustasio del Barrio 11:15 - 11:45 A random-projection based Gaussianity test for stationary process Juan A. Cuesta-Albertos 11:45 - 12:15 Probability bounds for model selection in ill posed inverse problems and active learning Carenne Ludeña ...... 10:45 - 12:15 Invited Session V-IV: Queues and Risk Processes Room 1.0.B05 Organizer: David Perry 10:45 - 11:15 Queues and risk models Jacques Resing

17 11:15 - 11:45 Two sided Markov-modulated reflection of Brownian motion. Applications to fluid queues Bernardo D’Auria 11:45 - 12:15 The idle period of the finite G/M queue with an interpretation in risk theory Andreas H. Lopker ...... 10:45 - 12:15 Invited Session V-V: Asset Allocation Room 1.0.B06 Organizer: Alejandro Balbás 10:45 - 11:15 Variance risk premium, economic risks, and the cross-section of expected returns Alfonso Novales 11:15 - 11:45 Optimal dividend policy with different regulations and risk measures Silviu Glavan 11:45 - 12:15 Optimal risk in marketing resource allocation Mercedes Esteban ...... 10:45 - 12:15 Invited Session V-VI: Scan and Spatial Test Statistics Room 1.0.B07 Organizer: Hock Peng Chan 10:45 - 11:15 K-scan for anomaly detection Ji-Meng Loh 11:15 - 11:45 A cluster identification framework illustrated by a filtering model for a earthquake occurrences Zhengxiao Wu 11:45 - 12:15 Statistical inference under spatial preferential sampling Zhengyuan Zhu ...... 10:45 - 12:15 Invited Session V-VII: Random Graphs, Random Networks and Epidemiology Room 1.0.B08 Organizer: Pascal Moyal 10:45 - 11:15 Diffusion and cascading behavior in random networks Marc Lelarge 11:15 - 11:45 Large graph limit for a SIR process in a random network with heterogeneous connectivity Jean-StéphaneDhersin 11:45 - 12:15 Some limit theory for special classes of graphs Susan Holmes ...... 10:45 - 12:15 Invited Session V-VIII: Distribution Theory of Runs and Patterns and its Applications Room 1.0.B09 Organizer: James C. Fu 10:45 - 11:15 Runs and scans in exchangeable trials with application to reliability Serkan Eryilmaz

18 11:15 - 11:45 Approximating probabilities for runs and patterns in i.i.d. and Markov dependent trials Brad C. Johnson 11:45 - 12:15 Approximating the extreme right-hand tail probabilities for distributions of runs and patterns James C. Fu

12:15 - 12:30 Break

12:30 - 14:00 Invited Session VI-I: Distributional Tests and Related Theory Room 1.0.B02 Organizer: Yongzhao Shao 12:30 - 13:00 Behaviour of change-point tests near the detection boundary Michael Stewart 13:00 - 13:30 Robust-eﬃcient test for exponentiality Jiqiang Guo 13:30 - 14:00 A probabilistic characterization for multivariate normality Yongzhao Shao ...... 12:30 - 14:00 Invited Session VI-II: Sequential Detection and Estimation IV Room 1.0.B03 Organizers: George Moustakides, Igor Nikiforov & Alex Tartakovsky 12:30 - 13:00 Minimax-Bayesian test for sequential testing of two composite hypothesis Boris Darkhovsky 13:00 - 13:30 Sequential nonparametric estimation of the drift in diﬀusion based on discrete-time observations Leonid Galtchouk 13:30 - 14:00 Tracking a threshold crossing stopping time over a Gaussian random walk through noisy observations Aslan Tchamkerten ...... 12:30 - 14:00 Invited Session VI-III: Methods for Functional Data Room 1.0.B04 Organizer: Cristian Preda 12:30 - 13:00 Wavelet-based estimation in functional linear regression with applications to life sciences Ana Maria Aguilera 13:00 - 13:30 Nonparametric functional regression with functional responses using Gaussian process models Heng Lian 13:30 - 14:00 Anticipated and adaptive prediction in functional discriminant analysis Cristian Preda ......

19 12:30 - 14:00 Invited Session VI-IV: Recent Contributions to Queueing, Inventory and Re- lated Fields Room 1.0.B05 Organizer: Shelemyahu Zacks 12:30 - 13:00 The M/G/1+G queue revisited David Perry 13:00 - 13:30 Ruin probability in a homogeneous insurance risk model Claude Lefèvre 13:30 - 14:00 Fluid EOQ model of perishable items, with intermittent high and low demand rates Shelemyahu Zacks ...... 12:30 - 14:00 Invited Session VI-V: Multiassets Financial Models Room 1.0.B06 Organizer: Ilya Molchanov 12:30 - 13:00 Portfolio optimization and multivariate Lévyprocesses Antonis Papapantoleon 13:00 - 13:30 Coherent multivariate risk measures and depth-trimming Ignacio Cascos 13:30 - 14:00 Symmetries of probability distributions in view of applications to multiasset derivatives pricing Ilya Molchanov ...... 12:30 - 14:00 Invited Session VI-VI: Discrete Probability Distributions Room 1.0.B07 Organizer: Pedro Delicado 12:30 - 13:00 The Aitchision simplex as a space of discrete probability distributions K. Gerald van den Boogaart 13:00 - 13:30 Definition, characterization and usefulness of the extended truncated Tweedie-Poisson model Josep Ginebra 13:30 - 14:00 Some general results about transforming weighted discrete distributions CélestineC. Kokonendji ...... 12:30 - 14:00 Invited Session VI-VII: Applied Probability in Biomedical Research Room 1.0.B08 Organizer: Wendy Lou 12:30 - 13:00 D2 statistics for word composition around replication origins of viral DNA Ming-Ying Leung 13:00 - 13:30 Exact distributions and sequential monte carlo for change points in brain imaging studies John Aston ...... 12:30 - 14:00 Invited Session VI-VIII: Spacings and their Applications Room 1.0.B09 Organizers: Joseph Glaz & RaúlJiménez

20 12:30 - 13:00 A weighted mean excess function approach to the estimation of Weibull-type tails Yuri Goegebeur 13:00 - 13:30 Stochastic properties of spacings based on order statistics Nuria Torrado 13:30 - 14:00 Spacings ratio empirical processes Paul Deheuvels

14:00 - 15:15 Lunch

15:15 - 16:15 Contributed Session III-I: Epidemic Models Room 1.0.B01 15:15 - 15:35 Understanding the effect of infectiveness on dose-response and epidemic model by stochastic orderings Isabel Ortega 15:35 - 15:55 A stochastic SIR epidemic model on a network of individuals with household structure David Sirl ...... 15:15 - 16:15 Contributed Session III-II: Asset Pricing and Options Room 1.0.B02 15:15 - 15:35 Option pricing and estimation under stochastic volatility with long-memory Alexandra Chronopoulou 15:35 - 15:55 Convergence of option rewards for multivariate price processes Robin Lundgren 15:55 - 16:15 Designing good deals in practice Raquel Balbás ...... 15:15 - 16:15 Contributed Session III-III: Stochastic Orders and Couplings Room 1.0.B03 15:15 - 15:35 Stochastic comparisons for time transformed exponential models Julio Mulero 15:35 - 15:55 Multivariate order based on extremality notion Henry Laniado Rodas 15:55 - 16:15 Markov couplings, stochastic orders, and stochastic relations Lasse Leskelä ...... 15:15 - 16:15 Contributed Session III-IV: Random Graphs and Computational Geometry Room 1.0.B04 15:15 - 15:35 A sex talk: The matchmaking paradox Iddo Eliazar

21 15:35 - 15:55 The distribution of the domination number of a family of random catch digraphs based on one-dimensional data Elvan Ceyhan 15:55 - 16:15 Computing weighted-mean trimmed regions in any dimension Karl Mosler ...... 15:15 - 16:15 Contributed Session III-V: Multivariate Analysis Room 1.0.B05 15:15 - 15:35 The sinh-arcsinhed t distributions Juan Francisco Rosco 15:35 - 15:55 On the γ-order generalized Gaussian Paula Camelia Trandafir 15:55 - 16:15 Estimation of the spectral probability measure Armelle Guillou ...... 15:15 - 16:15 Contributed Session III-VI: Limit Laws and Asymptotics of Algorithms Room 1.0.B06 15:15 - 15:35 Limit laws for maxima of a stationary random sequence with random sample size Maria da Gra¸caTemido 15:35 - 15:55 Some convergence results in a modified leader election algorithm Ravi Kalpathy 15:55 - 16:15 Long runs from a conditioned random walk and importance sampling algorithm for rare event simulation Michel Broniatowski ...... 15:15 - 16:15 Contributed Session III-VII: Analysis of Stochastic Processes Room 1.0.B07 15:15 - 15:35 On the Laplace transform of some functionals related to the variation of Brownian motion with drift Rafal Lochowski 15:35 - 15:55 On the distribution of a damped telegraph random process Antonio di Crescenzo 15:55 - 16:15 Error distribution of the ensemble Kalman filter update Andrey Kovalenko ...... 15:15 - 16:15 Contributed Session III-VIII: Queues Room 1.0.B08 15:15 - 15:35 Light-traffic analysis of queueing systems with train arrivals Koen de Turck 15:35 - 15:55 Stochastic approximation in a M/G/1 queue with vacations Karim Abbas

22 16:15 - 16:30 Coﬀee break

16:30 - 17:30 Contributed Session IV-I: Risk Models II Room 1.0.B02 16:30 - 16:50 A numerical method for expected penalty-reward function in a Markov-modulated jump-diffusion process Peter Diko 16:50 - 17:10 On a discrete time risk model with interest Maude Gathy ...... 16:30 - 17:30 Contributed Session IV-II: Markov Processes Room 1.0.B03 16:30 - 16:50 Convergence of quasi-stationary distributions of sequences of birth-death processes Damian Clancy 16:50 - 17:10 An urn model for population mixing and the phases within Tong Zhang 17:10 - 17:30 On the pdfs’ of the state sizes of a continuous time homogeneous Markov system with finite state capacities George Vasiliadis ...... 16:30 - 17:30 Contributed Session IV-III: Statistical Inference for Stochastic Processes Room 1.0.B04 16:30 - 16:50 Non-identifiability of the two-state markovian arrival process Pepa Ramirez-Cobo 16:50 - 17:10 Asymptotic theory of change diagnosis in the distribution of a Markov-modulated random sequence Kazutoshi Yamazaki 17:10 - 17:30 Maximum likelihood inference for processes killed at a threshold Enrico Bibbona ...... 16:30 - 17:30 Contributed Session IV-IV: Queues and Heavy Traffic Limits Room 1.0.B05 16:30 - 16:50 Controlled stochastic networks in heavy traffic: convergence of value functions Arka Gosh 16:50 - 17:10 Asymptotic analysis of traffic lights performance under heavy-traffic assumption Ekaterina Bulinskaya 17:10 - 17:30 Optimality of trunk reservation for an M/M/k/N queue with several types of customers and holding cost Eugene Feinberg

23 ...... 16:30 - 17:30 Contributed Session IV-V: Stochastic Control Room 1.0.B06 16:30 - 16:50 Changepoint model for high yield processes Mavroudis Eleftheriou 16:50 - 17:10 The stochastic goodwill problem: a monotone follower model with discretionary stopping Polly Lon 17:10 - 17:30 Irreversible capacity expansion with proportional and fixed costs Hessah Al-Motairi ...... 16:30 - 17:30 Contributed Session IV-VI: Methods for Functional Data Room 1.0.B07 16:30 - 16:50 Maxima of moving maxima of continuous functions Thomas Meinguet 16:50 - 17:10 Inference for the difference of two percentile residual life functions Alba Mar´ıaFranco Pereira 17:10 - 17:30 Functional data analysis of wave profiles Joaqu´ınOrtega ...... 15:15 - 16:15 Contributed Session IV-VII: Statistical Methods for Reliability Data Room 1.0.B08 16:30 - 16:50 Penultimate models for the reliability of series-parallel and parallel-series systems Paula Reis 16:50 - 17:10 New characterizations of multivariate lifetime distribution Rosario Rodr´ıguez-Griñolo ...... 16:30 - 17:30 Contributed Session IV-VIII: Time Series Room 1.0.B09 16:50 - 17:10 Time series segmentation by Cusum, AutoSLEX and AutoPARM methods Ana Laura Badagián 16:30 - 16:50 The power log-GARCH model Genaro Sucarrat 17:10 - 17:30 Sequential data-adaptive bandwidth selection for dependent discrete-time processes Ansgar Steland

17:30 - 17:45 Break

17:45 - 18:30 Plenary Talk: Michael Steele Auditorio Stochastic combinatorial optimization: from the TSP and MST to dogerpillars

24 Thursday, July 8th, 2010

9:30 - 10:15 Plenary Talk: Mihail Zervos Auditorio On the optimal stopping of one-dimensional Itˆodiﬀusion

10:15 - 10:45 Long coﬀee break

10:45 - 12:15 Invited Session VII-I: Stochastics and Finance I Room 1.0.B02 Organizer: Olympia Hadjiliadis 10:45 - 11:15 General theory of the numeraire change for exotic options Jan Vecer 11:15 - 11:45 Heat equation, first passage boundary problems and orthogonal polynomial Gerardo Hernández-del-Valle 11:45 - 12:15 Maximum drawdown of a jump-difussion process and pricing PIDE’s Libor Pospisil ...... 10:45 - 12:15 Invited Session VII-II: Scan Statistics Room 1.0.B03 Organizer: George Haiman 10:45 - 11:15 Two-dimensional variable window scan statistics for Poisson process Jie Chen 11:15 - 11:45 Scan statistics for i.i.d. normal random variables Joseph Glaz 11:45 - 12:15 Fitting a 1-dependent model to stationary data with applications to scan statistics George Haiman ...... 10:45 - 12:15 Invited Session VII-III: Statistics of Complex Systems Room 1.0.B04 Organizer: Iddo Eliazar 10:45 - 11:15 Universal generation of fractal statistics Iddo Eliazar 11:15 - 11:45 A vibrational shortcut to the mean first passage time problem Shlomi Reuveni 11:45 - 12:15 Modelling extreme bursts above thresholds in a fractional stable toy model for natural complex systems Nicholas Watkins ...... 10:45 - 12:15 Invited Session VII-IV: Stochastic Modeling and First Exit Time Applications Room 1.0.B05 Organizer: Christos H. Skiadas

25 10:45 - 11:15 Stochastic modeling and the first exit time problem Christos H. Skiadas 11:15 - 11:45 Modeling and analysis of demographic data of Spain George Matalliotakis 11:45 - 12:15 Stochastic processes implementation methodology for life table data analysis of the population of Portugal Maria Vardoulaki ...... 10:45 - 12:15 Invited Session VII-V: Analytic Combinatorial Probability Room 1.0.B06 Organizer: Hosam Mahmoud 10:45 - 11:15 Generalized stirling permutations, families of increasing trees and urn models Alois Panholzer 11:15 - 11:45 Suffix trees: A survey, and future challenges Mark Daniel Ward 11:45 - 12:15 Analysis of swaps in radix selection Hosam Mahmoud ...... 10:45 - 12:15 Invited Session VII-VI: Dependence and Predictability Room 1.0.B07 Organizer: JoséMiguel Angulo Ibáñez 10:45 - 11:15 Effect of data transformations on predictive risk indicators Francisco Javier Alonso 11:15 - 11:45 Multiplicative Kalman filter Mathieu Kessler 11:45 - 12:15 Comparative analysis of space-time factoras, copulas, and BME methods in multivariate modelling George Christakos ...... 10:45 - 12:15 Invited Session VII-VII: Markov Chain Modelling Room 1.0.B08 Organizer: JoséLuis Palacios 10:45 - 11:15 Branching processes in random walks Haiyan Chen 11:15 - 11:45 Sum rules for hitting times of Markov chains JoséMiguel Renom 11:45 - 12:15 Random walks on graphs using local degree information Satoshi Ikeda

12:15 - 12:30 Break

12:30 - 14:00 Invited Session VIII-I: Stochastic and Finance II Room 1.0.B02 Organizer: Olympia Hadjiliadis

26 12:30 - 13:00 Optimal portfolios and admissible strategies in Lévy-driven markets Jose Figueroa-Lopez 13:00 - 13:30 The optimal method for pricing bermudan options by simulation Carlos Velasco 13:30 - 14:00 Pricing and hedging in affine models with jump to default Alexander Wugalter ...... 12:30 - 14:00 Invited Session VIII-II: Scan Statistics: Methods and Applications Room 1.0.B03 Organizer: Jie Chen 12:30 - 13:00 Scalable Bayesian event detection and visualization Daniel B. Neill 13:00 - 13:30 Continuous, discrete and conditional scan statistics Wendy Lou 13:30 - 14:00 Detection of spatial clustering through grouping and average likelihood ratio test statistics Hock Peng Chan ...... 12:30 - 14:00 Invited Session VIII-III: Telecommunication Networks Room 1.0.B04 Organizer: Sergei Zuyev 12:30 - 13:00 Connection lenghts in spatial stochastic networks: scaling limits and Monte-Carlo methods Florian Voss 13:00 - 13:30 A binary inference framework for optimal channel selection in distributed sniffer networks Rong Zheng 13:30 - 14:00 Thinning-stable point processes: new model in telecommunications Sergei Zuyev ...... 12:30 - 14:00 Invited Session VIII-IV: On some special stochastic processes and related distributions Room 1.0.B05 Organizer: Kenneth J. Hochberg 12:30 - 13:00 On some fractional point processes Enzo Orsingher 13:00 - 13:30 A survey on the pseudo-process driven by a high-order heat-type equation AiméLachal 13:30 - 14:00 Structural invariance for a class of probability laws and a related branching particle system Kenneth J. Hochberg ...... 12:30 - 14:00 Invited Session VIII-V: Probability and Algorithms Room 1.0.B06 Organizer: Omiros Papaspiliopoulos

27 12:30 - 13:00 Gibbs sampling methods for population processes in infinite dimensional models Matteo Ruggiero 13:00 - 13:30 Making black boxes out of black boxes - the Bernoulli factory problem and its extensions Krzysztof Latuszynski 13:30 - 14:00 Monte Carlo methods on sensitivities estimation of American options Nan Chen ...... 12:30 - 14:00 Invited Session VIII-VI: Bayesian reliability Room 1.0.B07 Organizer: Antonio Pievatolo 12:30 - 13:00 Bayesian estimation of degradation model defined by a Wiener process Fabrice Guerin 13:00 - 13:30 A Bayesian reliability model for repairable systems: an application to software data Michael Wiper 13:30 - 14:00 A Bayesian hidden Markov model for software failures Antonio Pievatolo ...... 12:30 - 14:00 Invited Session VIII-VII: Random Fields Room 1.0.B08 Organizer: Evgeny Spodarev 12:30 - 13:00 Rice methods for the maximum of a Gaussian random field Jean-Marc Azais 13:00 - 13:30 CLT for excursion sets of dependent random fields Evgeny Spodarev 13:30 - 14:00 Max-stable random fields and negative-definite functions Zakhar Kabluchko

14:00 - 15:15 Lunch

28 Abstracts

Plenary Talks

Model uncertainty in financial risk management. Speaker: Paul Embrechts, ETH Zurich, Switzerland. The current financial crisis puts into question the understanding of the valuation of complex credit derivatives like Collateralized Debt Obligations. In this talk I will take a critical look at this issue and give examples, mainly from the realm of Multivariate Extreme Value Theory, of where model uncertainty in financial risk management plays a crucial role. Besides giving a short non-technical discussion of the topic “Mathematics and the financial crisis”, I will highlight some mathematical research triggered by the crisis.

Estimating boundary measures of general sets. Speaker: Ricardo Fraiman, Universidad de San Andrés,Argentina, and Universidad de la República, Uruguay. We deal with a subject in the interplay between nonparametric statistics and geometric measure theory. The d measure L0(G) of the boundary of a compact set G ⊆ R (with d ≥ 2) can be formally defined, via a simple limit, by the so-called Minkowski content. We study the estimation of L0(G) from a sample of random points inside and outside G. The sample design assumes that, for each sample point, we know (without error) whether or not that point belongs to G. Under this design we suggest a simple nonparametric estimator and investigate its consistency properties. The main emphasis in this problem is on generality. So we are especially concerned with proving the consistency of our estimator under minimal assumptions on the set G. In particular, we establish a very mild shape condition on G under which the proposed estimator is consistent in L2 and almost surely. Roughly speaking, such condition establishes that the set of “very spiky” points at the boundary of G must be “small”. This condition is carefully analyzed, providing some equivalent statements as well as some sufficient conditions for it. Several examples are discussed.

Spatial Bayesian quantile regression: application to study the impact of climate change on tropospheric ozone. Speaker: Montserrat Fuentes, North Carolina State University, USA. Smog is a term used to describe air pollution that is a result of the interaction of sunlight with certain chemicals in the atmosphere. One of the primary components of smog is ozone. While ozone in the stratosphere protects earth from harmful UV radiation, ozone on the ground (tropospheric ozone) is hazardous to human health. This tropospheric ozone is one of the six criteria pollutants regulated by the US EPA under the Clear Air Act, and has been linked with several adverse health effects. Due to the strong dependence on weather conditions, ozone may be sensitive to climate change and there is great interest in studying the potential effect of climate change on ozone, and how this change may affect public health. In this presentation, I introduce statistical methods to study and quantify the impact of climate change on ozone, and the potential implications that may have for air quality regulation. More specifically, we develop a Bayesian spatial model to predict ozone under different meteorological conditions, and use this model to study spatial and temporal trends and to forecast ozone concentrations under different climate scenarios. We propose a spatial quantile regression model that does not assume normality and

31 allows the covariates to aﬀect the entire conditional distribution, rather than just the mean. The conditional distribution is allowed to vary from site-to-site and is smoothed with a spatial prior. We apply our model to summer ozone from 1997-2005 in the Eastern US, and use deterministic climate models to project ozone under future climate conditions. Our analysis suggests that holding all other factors ﬁxed, an increase in daily average temperature will lead to the largest increase in ozone in the Industrial Midwest and Northeast. In collaboration with Brian Reich (North Carolina State University) and David Dunson (Duke University).

Probability and the analysis of algorithms: examples and open problems. Speaker: Robin Pemantle, University of Pennsylvania, USA. I will survey a number of algorithms that make essential use of randomness, in the sense that randomness is necessary to achieve the best rigorous performance bounds. Analysis of the running times of these algorithms require probabilistic methods beyond the naive methods that are well known in the ﬁelds of application (e.g., searching, linear programming, satisﬁability testing, factoring). While discussing these, I will point out a number of related open problems.

A method for estimating threshold crossing time with application to climate change Speaker: Victor de la Pe˜na, Columbia University, USA. Climate projections for the 21st century exhibit gradual changes in many variables such as temperature and precipitation, which are of consequences to society. Planners and decision-makers may want to use such information for the purposes of developing strategies for adaptation and/or mitigation. In particular, they may want to estimate when the gradual changes in a climate variable might reach a certain threshold and then attach to such information a measure of uncertainty. Here propose a method based in projections generated by multiple models. This method is shown to have better predictive skill (with respect to mean square error) than the commonly used method. As an application we look at the projected reduction in rainfall in two subtropical regions: the US and the Mediterranean.

Stochastic combinatorial optimization: From the TSP and MST to dogerpillars. Speaker: J. Michael Steele, University of Pennsylvania, USA. Perhaps the two most famous problems in Euclidean combinatorial optimization are the traveling salesman problem (TSP) where one considers the shortest tour through n points, and the minimal spanning tree (MST) problem where one considers the tree of minimal length that covers the n points. In this lecture we ﬁrst review some of the extensive work that has been done on the stochastic versions of these problems where the n points are chosen independently from a given distribution. We then look at problems that interpolate between the TSP and the MST; the simplest example being the “spanning caterpillar”. In graph theory, a caterpillar is a graph which has a path that when removed leaves only a collection of disjoint “stars”. We then sketch a proof of the fundamental theorem on spanning caterpillars - the analog of the Beardwood, Halton, Hammersley theorem for the TSP. Finally, we consider a new rich class of spanning graphs that are called “dogerpillars”, or more precisely k-dogerpillars. Despite the silly name, these graphs provide a satisfying way to interpolate the full range of graphs between the TSP and the MST. As a consequence, they unify and extend our understanding of the probability

32 theory of the TSP and MST.

Optimal stopping of a one-dimensional Itôdiffusion. Speaker: Mihail Zervos, London School of Economics, UK. We consider a one-dimensional Itôdiffusion X with values in an interval I. In particular, we assume that X satisfies the stochastic differential equation

dXt = b(Xt) dt + σ(Xt) dWt in the interior int I = ]α, β[ of I, where b, σ : int I → R are Borel-measurable functions, W is a standard one- dimensional Brownian motion, and −∞ ≤ α < β ≤ ∞. We allow for the endpoints α and β to be inaccessible or absorbing. The objective of the discretionary problem that we study aims at maximising the performance index Z τ Ex exp − r(Xt) dt f(Xτ )1{τ<∞} 0 over all stopping times τ, where the reward function f : I → R+ and the discounting rate function r : I → R+ are Borel-measurable. We derive a simple necessary and sufficient condition for the value function v of this problem to be real-valued. In this case, we show that v is the difference of two convex functions, and we prove that it satisfies the variational inequality

1 max σ2v00 + bv − rv, f − v = 0 (1) 2 in the sense of distributions, where f is the upper semicontinuous envelope of f. Conversely, we establish boundary conditions at the endpoint α and β that a solution of (1) should satisfy to identify with the value function v. Furthermore, we derive a generalisation of the so-called “principle of smooth ﬁt” that can be used to obtain explicit solutions in special cases of the general problem. This is a joint work with Damien Lamberton.

Invited Talks

Wavelet-based estimation in functional linear regression with applications to life sciences. Speaker: Ana M. Aguilera, Universidad de Granada, Spain. Co-authors: Manuel Escabias, Francisco A. Ocaña,Mariano J. Valderrama. The power of functional data analysis to estimate a set of curves from others involved is studied in this work in the context of life sciences. More specifically, the objective is to predict the degree of lupus in patients suffering from this autoimmune disease from their level of stress experienced daily. Stress curves have a a strong local behavior (high peaks with great variability) and missing data those days that a patient does not answer the corresponding test. Taking into account this special pattern of the sample curves, wavelet smoothing from their daily observations is considered. After using an appropriate thresholding rule, functional PCA is used to reduce the dimension and to solve problems related with the high correlation between wavelet coefficients of lupus and stress curves. This way the functional linear regression model with functional response is reduced to multivariate regression of a set of principal components of the functional response (lupus) on a set of principal components of the functional predictor (stress). In a second step the functional residuals of this model are estimated from past evolution of the response. To avoid a trivial functional PCA with too high variability accumulated by the first principal component , we work with standardized lupus and stress derivatives instead of the raw data. The problem of model selection is solved by using a criterion that selects those pairs of response-predictor principal components that explain the highest proportions of response variability.

Effect of data transformations on predictive risk indicators. Speaker: Francisco Javier Alonso, Universidad de Granada, Spain. Co-authors: Maria del Carmen Bueso, Jose Miguel Angulo. Risk indicators used in many applications usually involve certain transformations of the variables of interest, such as averages or maxima over given time periods or spatial regions, threshold exceedances, etc., or a combination of them. A common practice is to predict these indicators by applying the same type of transformation on the sample data, that is, the “historical” values of the same indicators are used as the sample information set. In this work we study, for different indicators and considering a flexible covariance model separating fractal dimension and memory, the loss of information derived from the transformations defining the sample set. The evaluations and comparisons are performed in terms of predictive mutual information based on Shannon’s entropy. The results obtained for different scenarios suggest that, depending on the type of risk indicator considered and the dependence structure of the process of interest, the changes in terms of predictive information using diverse transformations of the observations may be substantial.

Modeling fiber reinforced polymers. Speaker: Hellen Altendorf, Mines Paris Tech, France. Co-authors: Dominique Jeulin. The increasing interest in fibrous materials expands to a large variety of use cases, as for example in the enclosure of aircrafts, boats and cars, but also wound disinfection tissues and thermal isolations make use of fibrous media.

35 The macroscopic properties of these materials are highly influenced by the geometry of the fiber component, in particular by the direction distribution. Material properties can be optimized using numerical simulations and fiber models fitted to the real structure. Most of the existing approaches model fibers as cylinders (dilated Poisson line process, random sequential absorption for cylinders or falling cylinder simulation), which limits the material to straight fiber segments and to low volume fractions. Fiber reinforced polymers or non-woven with high fiber volume fraction and non-overlapping, even bending fibers request other stochastic models. We present an approach modeling fiber cores as ball chains, created by random walks using the multivariate von Mises-Fisher direction distribution. The fiber cores are dilated a posteriori with radii assigned to each ball during the walk. To achieve a non-overlapping system we apply a force biased approach to the fiber cores. To every ball in the chains, we assign a force, depending on the overlap with other fibers and on the attraction of neighbor balls in the same fiber. The forces are minimized locally. The initial configuration and fiber volume fraction determine, if the final configuration results in a total hardcore system.

Trimming methods in model validation Speaker: Pedro César Alvarez´ Esteban, Universidad de Valladolid, Spain. We say that two probabilities are α-similar if they are contaminated versions (up to an α fraction) of the same common probability. We show how this model can be assessed using minimal distances between sets of trimmed probabilities. We study the main properties of these sets and use the L2-Wasserstein distance to obtain uniqueness and consistency results. Empirical versions of these probabilities are used to statistically assess the previous model and a bootstrap methodology based on what we call overfitting effect is developed. Roughly speaking, this overfitting effect says that if two random samples of the same probability distribution are partially trimmed to make them as similar as possible, then you should be able to distinguish these pair of trimmed samples from any other pair of non-trimmed samples of the same distribution. Finally, we provide some simulation results that illustrate the behavior of this procedure for finite samples.

Two-Stage Inference Methods for “Large p, Small n” Scenarios: Part II. Speaker: Makoto Aoshima, University of Tsukuba, Japan. High Dimension, Low Sample Size (HDLSS) data are emerging in various areas of modern science such as genetic microarrays, medical imaging, text recognition, finance, chemometrics, and so on. In this talk, we offer effective strategies to determine the sample size so as to satisfy a specified accuracy for a variety of inference in HDLSS context. We first consider Principal Component Analysis (PCA). Yata and Aoshima (2010a; Commun. Statist.- Theory Meth.) and Yata and Aoshima (2010b,c; J. Multiv. Anal.) showed that the sample covariance matrix has various types of geometric representations in HDLSS context. With the help of the geometric representations, they proposed new methodologies called “noise-reduction methodology”and “cross-data-matrix methodology” to draw statistical inference from a HDLSS dataset. By using those methodologies, we estimate eigenvalues, PC directions and PC scores effectively in HDLSS data situations. Next, we consider a two-stage elimination procedure to select significant subsets of associated variables from a HDLSS dataset. We emphasize that a two- stage procedure is a strong tool to reduce the dimensionality with redundant variable elimination. By using the proposed two-stage elimination procedure as a preprocessor, we implement the noise-reduction methodology to develop discriminant analysis in HDLSS context. We also consider cluster analysis in HDLSS context. We apply

36 the cross-data-matrix methodology to a mixture model to classify a dataset into several clusters. We demonstrate how the new methodologies give a useful performance by using HDLSS data from a microarray study of prostate cancer. Further, we consider regression analysis and model selection criteria for AIC in HDLSS context.

Parameter estimation in multiple hidden i.i.d. models from biological multiple alignment. Speaker: Ana Arribas Gil, Universidad Carlos III de Madrid, Spain. Models for pairwise alignment of DNA sequences based on the classical TKF (Thorne, Kishino and Felsenstein 1991) insertion and deletion process fit into the pair-Hidden Markov Model (pair-HMM), that is, the alignment is a hidden Markov chain which emits the two observed DNA sequences. Many efficient algorithms have been developed in the field of bioinformatics to estimate alignments and evolution parameters in this context. Also, from a theoretical point of view, the statistical properties of the estimators computed by these algorithms in the pair-HMM have been investigated. The challenge is now to extend the existent algorithms and results to the case in which we deal with multiple alignment, that is, when we want to align a certain number (> 2) of sequences related by a given phylogenetic tree. We present here a formulation of the multiple alignment model that define a new kind of hidden variable models and investigate asymptotic properties of estimators under this model.

Exact distributions and sequential monte carlo for change points in brain imaging studies. Speaker: John Aston, University of Warwick, UK. Co-authors: Christopher Nam, Adam Johansen. Quantifying the uncertainty in the locations of change points is a topic of signiﬁcant interest. However, when additional spatial information is also available such that change points are likely to occur at similar times in similar locations, detection can be enhanced and uncertainty reduced. A new methodology is proposed to quantify change points in massive data sets such as functional brain imaging studies using hidden Markov models. This method is based on using Markov chain imbedding to generate exact distributions of change point locations for particular parameter estimates of the HMM and then using sequential Monte Carlo to sample the parameter distribution. Using this approach dramatically reduces the search space, as state estimates for each time point are no longer required, particularly if only a small number of change points likely occur.

Asymptotically optimal dynamic pricing for network revenue management. Speaker: Rami Atar, Technion, Israel. Co-authors: Martin Reiman. We consider a dynamic pricing problem that arises in a revenue management context, involving several resources and several demand classes, each of which uses a particular subset of the resources. The arrival rates of demand are determined by prices, that can be dynamically controlled. The problem, set on a finite time horizon, is to choose a policy to maximize the expected total reward. When viewed in diffusion scale, the problem gives rise to a diffusion control problem whose solution is a Brownian bridge. We prove diffusion-scale asymptotic optimality of a dynamic pricing policy that mimics the behavior of the Brownian bridge.

37 Rice method for the maximum of a Gaussian random field. Speaker: Jean-Marc Aza¨ıs, Universitéde Toulouse, France. Looking, among the local maxima of a random field, to those that are actually a global maxima, we obtain an implicit formula for the density of the maximum of a regular process on a regular set. This formula can be used to give bounds to the density to obtain non-asymptotic bounds for the distribution of the maximum as well as expansion to the second order. We make some comparison with other methods.

Testing hypotheses for semi-Markov processes. Speaker: Vlad Stefan Barbu, Universitéde Rouen, France . Co-authors: Ghislaine Gayraud. This article is concerned with hypotheses testing for semi-Markov chains. The goal is to provide a test procedure which is able to distinguish between two semi-Markov chains. To insure more generality to our approach, we consider the neighborhoods of two semi-Markov kernels, built from a pseudo-distance based on the Hellinger affinity. Afterwards, we propose a test statistics of log-likelihood ratio type. Our main interest is to control the performance of such a test; to this purpose, we provide exponential upper bounds for the first-type and second-type errors.

Asymptotics for model checking methods based on trimming. Speaker: Eustasio del Barrio, Universidad de Valladolid, Spain. This talk introduces an analysis of similarity of distributions based on measuring some distance between trimmed distributions. Our main innovation is the use of the impartial trimming methodology, already considered in robust statistics, which we adapt to the setup of model checking. By considering trimmed probability measures we introduce a way to test whether the core of the random generator underlying the data ﬁts a given pattern. Instead of simply removing mass at non-central zones for providing some robustness to the similarity analysis, we develop a data-driven trimming method aimed at maximizing similarity between distributions. Dissimilarity is then measured in terms of the distance between the optimally trimmed distributions. Our main choice for applications is the Wasserstein metric, but other distances might be of interest for diﬀerent applications. We provide illustrative examples showing the improvements over previous approaches and give the relevant asymptotic results to justify the use of this methodology in applications.

Moderate deviations for word counts in biological sequences. Speaker: Sarah Behrens, Max Planck Institute for Molecular Genetics, Germany. Co-authors: Matthias Löwe. Recent progress in DNA and protein sequencing stressed the necessity of having statistical methods for the analysis of biological sequences. One probabilistic approach to recognize special features of DNA or protein sequences is to identify words or motifs which occur significantly often or rarely. We derive a moderate deviation principle for word counts (which is extended to counts of multiple patterns) in biological sequences under different models: i.i.d. letters, homogeneous Markov chains of order 1 and m respectively, and - in view of the codon structure of

38 DNA sequences - Markov chains with three diﬀerent transition matrices. This enables us to approximate p-values for the number of word occurrences in DNA and protein sequences in a new manner.

Multivariate likelihood ratio ordering of ordered data. Speaker: F´elixBelzunce, Universidad de Murcia, Spain. Co-authors: Selma Gurler, Jos´eM. Ruiz. Recently Balakrishnan, Belzunce, Hami and Khaledi (2009) give some results for the comparison in the multivariate likelihood ratio order of vectors of generalized order statistics. This result covers, as a particular case, order statistics from independent and identically distributed observations. In this talk we present some additional results for the comparisons in the multivariate likelihood ratio order of order statistics from independent but not necessarily identically distributed observations and for the case of possible dependent observations. Applications of these results to provide comparisons of conditional order statistics are also given.

Inference for context-dependent nucleotide substitution models. Speaker: Jean Bérard, UniversitéClaude Bernard - Lyon 1, France. Co-authors: Laurent Guéguen. Stochastic models of nucleotide substitution processes usually make the assumption that distinct sites along the DNA sequence evolve independently. However, context-dependent effects, e.g. CpG hypermutability, are known to affect substitution probabilities. Taking into account such context-dependent effects in phylogenetic inference is a challenging task, since most efficient computational techniques rely on the assumption of independence between sites. In this talk, we describe a family of context-dependent substitution models for which, thanks to the special form of the resulting dependency structure, computational methods developed for models with independently evolving sites can be adapted to produce efficient inference methods. An application to the detection of hypo-methylated islands in DNA sequences is discussed.

Multivariate uniformity tests for the case of unknown support. Speaker: JoséR. Berrendero, Universidad Autónomade Madrid, Spain. Co-authors: Antonio Cuevas, Beatriz Pateiro-López. Given a random sample of independent multivariate observations, we consider the problem of testing the hypothesis of uniformity on an arbitrary compact support. We build a test based on the use of multivariate spacings as those studied in Janson (1987). The test can be adapted to the case when the support is unknown, provided that it fulfils a mild shape condition. Some techniques borrowed from set estimation theory turn out to be useful in this case. The consistency properties of the test are analyzed and its performance is checked through a small simulation study. We discuss the numerical problems involved in the practical calculation of the maximal spacing, which is required to obtain the test statistic. Alternative approaches to deal with the same testing problem are also briefly addressed.

39 Hybrid Monte-Carlo in high dimensions. Speaker: Alexandros Beskos, University College London, UK. Co-authors: Natesh Pillai, Gareth Roberts, Andrew Stuart, JesúsM. Sanz-Serna. We have investigated algorithmic properties of Hybrid Monte-Carlo (HMC) in high dimensions. In the simplified scenario of “independent and identically distributed” target distributions we have found that the asymptotically optimal acceptance probability, for dimensionality growing to infinity, is 0.651 (up to three decimal places), irre- spective of the particular (i.i.d.) target. We have also worked on a semi-implicit version of the leapfrog integrator, which is relevant for target distributions defined as a change of measure from Gaussian laws arising in applications. We illustrate that implementation of the semi-implicit version of the integrator in such a context allows for the construction of a well-defined HMC algorithm in infinite-dimensional Hilbert spaces.

Asymptotic finite-time ruin probabilities for a class of path-dependent claim amounts using Poisson spacings. Speaker: Romain Biard, UniversitéLyon 1, France. Co-authors: Claude Lefèvre,StéphaneLoisel, Haikady N. Nagaraja. In the compound Poisson risk model, several strong hypotheses may be found too restrictive to describe accurately the evolution of the reserves of an insurance company. This is especially true for a company that faces natural disaster risks like earthquake or flooding. For such risks, claim amounts are often inter-dependent and they may also depend on the history of the natural phenomenon. The present paper is concerned with a situation of this kind where each claim amount depends on the previous interclaim arrival time, or on past interclaim arrival times in a more complex way. Our main purpose is to evaluate, for large initial reserves, the asymptotic finite-time ruin probabilities of the company when the claim sizes have a heavy-tailed distribution. The approach is based more particularly on the analysis of spacings in a conditioned Poisson process.

Set and set properties estimation. Speaker: Gérard Biau, UniversitéPierre et Marie Curie – Paris VI, France. Co-authors: BenoˆıtCadre, Bruno Pelletier. We study the two problems of reconstructing a set S and of estimating its number of connected components, from random points of S drawn from some probability measure. We focus on the certainly most simple set estimator defined as the union of balls centered at the random points. Second, we propose a graph-based estimator of the number of connected components of S. Using tools from Riemannian geometry, and under mild analytic conditions on the underlying density of the data, we derive the exact rate of convergence of this set estimator and prove the consistency of the estimator of the number of connected components. Statistical applications include density support estimation and estimation of the number of clusters in data partitioning.

Local motif detection in biological networks based on Poisson approximation. Speaker: Etienne Birmel´e, Universit´ed’Evry,´ France. The statistical study of real networks, that is networks obtained from sociological or biological data for instance,

40 has become a major field of interest in the last decade. In particular, it is possible to consider that networks are built from small functional units called motifs, which can be found by looking for small patterns which are significantly over-represented in the network of interest. We propose a new approach for motif detection by looking for patterns that are locally over-represented with respect to their sub-patterns. We define a general random graph model, whose parameters can be inferred, and show that under that model, the p-value of a local over-representation can be evaluated by using Poisson approximations. We apply our procedure to simulated and biological data and show that the known biologically relevant motifs are found again. Moreover, our method drastically reduces the computation time when taking the sub-patterns into account and gives some more information about the motifs it finds.

Optimal insurance with counterparty default risk. Speaker: Enrico Biffis, Imperial College London, UK. Co-authors: P. Millossovich. We study the design of optimal insurance contracts when the insurer can default on its obligations. We model default as arising endogenously from the interaction of the insurance premium, the indemnity schedule, and the evolution of the insurer’s assets. We allow for different forms and degrees of dependence between the insured’s wealth and the default event, to understand the joint effect of insolvency risk and background risk on efficient contracts. The results may shed light on the aggregate risk retention schedules observed in catastrophe reinsurance markets. They can also assist in the design of (re)insurance programs and in capital modeling exercises that allow for counterparty default risk.

CLT for multiple integrals with respect to the empirical process. Applications to the Wasser- stein test. Speaker: HélèneBoistard, UniversitéToulouse 1, France. In this talk, we will give results about weak convergence of multiple stochastic integrals with respect to the empirical process (cf, e.g., Major 2006). A stochastic integral with respect to the Brownian bridge is introduced to express the limit in a unified way for both the degenerate and non degenerate cases (cf. Boistard and del Barrio 2009). These results are closely related to well-known asymptotic results on U-statistics. Some contiguity results allow us to study the local efficiency of tests based on double integrals with respect to the empirical process, in the framework of Gaussian shifts. These tools will then be applied to study the local asymptotic power of the Wasserstein normality test.

The Aitchison simplex as a space of discrete probability distributions. Speaker: K. Gerald van den Boogaart, TU Bergakademie Freiberg, Germany . Co-authors: Juan Jos´eEgozcue, Vera Pawlowsky-Glahn. Like a composition, a probability distribution on a discrete support is given by a set of positive numbers adding to 1. Compositional data analysis uses a Hilbert space structure on such a set, called the Aitchison simplex. The same structure can be applied to the set of all probability measures with a discrete support. Many concepts of probability theory and statistics show up as algebraical and analytical properties of this new Hilbert space

41 structure. Probability measures are vectors, the uniform distribution is the origin, likelihoods and densities are vector differences, exponential families are affine subspaces, sufficient statistics form a basis, Bayesian theorem is addition, replication is multiplication, Fisher information is built into the spaces metric, the Bayesian principle is an inherent property of the space, independence corresponds to direct sums of spaces, and the conditional probabilities are elements of quotient space. The talk will introduce this new Hilbert space view on discrete probability distributions. A special example will be the zero inflated Poisson distribution.

Sequential detection of change-points in state-space models. Speaker: Boris Brodsky, Central Economics and Mathematics Institute, Russia. The problem of sequential detection of spontaneous changes in equations for unobserved state variables and observations of linear and nonlinear multivariate state-space models is considered. We consider the case of new additive terms and the case of changing coefficients of these equations. The proposed approach is genuinely nonparametric: distributions of random noises in equations for state variables and observations are unknown to us. This is the main difference from existing methods of change-point detection in state-space models (Willsky (1976), Basseville and Nikiforov (1993), Zhang (1991), Lai (1998, 2001), Fuh (2006)) in which the Gaussian distributions of random noises are usually assumed. The statement of the problem and main assumptions are given. The nonparametric method uses the idea of the moving window of observations. In a first theorem the exponential rate of convergence to zero for the type 1 error probability (a wrong decision about a change) is proved. In a second theorem we consider the type 2 error probability and the normalized (by the volume of the moving window) delay time in change-point detection. The exponential rate of convergence to zero for the type 2 error probability is proved and almost sure convergence of the normalized delay time to a certain constant dependent on parameters of the proposed method is demonstrated. Experimental study includes Monte Carlo examples of sequentially detected changes in coefficients of linear and nonlinear state-space models. An application to the problem of sequential detection of structural changes in the state-space model of the exchange rate dynamics is considered.

On Bayesian analysis in multistage designs. Speaker: Pierre Bunouf, CNRS - Universitéde Rouen, France. Based on a formulation of Bayes’ rule which integrates the design information, a new Bayesian approach to multistage analysis is considered. Prior is derived using Jeffreys’ criterion on likelihood associated with the design information. As a notable result, the prior for sequential Bernoulli design asymptotically converges toward the Jeffreys prior in Pascal sampling model. In hypothesis testing, the Bayes factor as posterior-based evidential measure can be generalized to multistage designs, so that the decision boundaries reflect equal evidence for hypotheses over stages. The property of bias correction of the prior is used in point estimation for a proportion. The transposition of the beta parameters of the Haldane and the uniform priors in fixed binomial experiments yields bias-corrected versions of the mean and the mode estimators in multistage designs.

Assessing ARMA models for stationary time series by transforming accumulated residues pro-

42 cesses. Speaker: Enrique M. Cabaña, Universidad de la República,Uruguay. Co-authors: Alejandra Cabaña. The transformation of processes has shown to be a fruitful tool in developing goodness-of-fit tests for independent samples and regression models. In the first case, the process to be transformed is the empirical process of the sample, and in the second one, a process of accumulated residues. In both cases, the transformation provides a new process able to detect any departure from the null hypothesis of model fit, and customised to show efficiently the departures in a given direction chosen by the user. The convergence under the null hypothesis of fit of the empirical process to a Brownian bridge (or its L2 projection on a known subspace when parameters are estimated) plays a central role in the heuristic and technical arguments applied for the transformation. When dealing with regression models, the accumulated residues process has similar asymptotic properties. We show that in the case of ARMA models, the behavior of a marked residues process leads to construct consistent tests for ARMA(p, q) models, focused on ARMA(p + 1, q) and ARMA(p, q + 1). The resulting tests are compared in terms of power with other included in the statistical literature, including the AR tests based on the m-th root of the determinant of the m-th autocorrelation matrix by Peñaand Rodr´ıguez(2002) and the test based on the discrepancy between the standardized spectral distribution and its sample estimate proposed by Anderson, Lockhart and Stephens (2004).

Riemannian manifold Hamiltonian Monte Carlo and population MCMC methods for estimating Bayes factors. Speaker: Ben Calderhead, University of Glasgow, UK. Co-authors: Mark Girolami. The task of Bayesian model comparison over statistical models is fraught with diﬃculties. For example, the required target densities may be high dimensional, multimodal and strongly correlated, and drawing samples can consequently be an extremely challenging task. I shall introduce Riemannian Manifold Hamiltonian Monte Carlo (RM-HMC) for addressing this problem. RM-HMC is an extension of the Hybrid Monte Carlo method and can be employed to sample from high-dimensional and strongly correlated probability densities. It exploits the natural Riemannian structure of the parameter space of statistical models, which allows the algorithm to automatically adapt to local correlations and is thus self-tuning. Finally I shall demonstrate how RM-HMC may be embedded within a population MCMC framework to allow sampling from multimodal posterior distributions, while simultaneously obtaining the required samples to accurately estimate marginal likelihoods via thermodynamic integration.

Visibility estimates in the Boolean model. Speaker: Pierre Calka, Universit´eParis V, France.

d A germ-grain model is constructed in R , with spherical or convex and compact grains. The visibility function is the length of the largest segment emanating from the origin and contained in the unoccupied phase of the model. We study the distribution of this variable in any dimension and in some particular asymptotic settings. Comparison with the same model in the hyperbolic disk will be discussed.

43 Stochastic iterative dynamic programming applied to optimal control problems. Speaker: Héctor Cañada-Jaime, Universidad Carlos III de Madrid, Spain. Co-authors: Rosario Romera. In this work an approximate dynamic programming approach to deal with optimal control problems in diffusion processes is developed. The diffusion processes are that of the class of non-linear stochastic differential equations with boundary conditions. Monte Carlo Techniques and discrete-time numerical approximations based on the Euler-Maruyama scheme are used. Preliminary analysis of the error and convergence properties that support the algorithm are presented. An illustrative example is included to highlight potential applications of our approach.

Linear discrimination under heteroscedasticity. Speaker: Javier Cárcamo, Universidad Autónomade Madrid, Spain. Co-authors: JoséRamónBerrendero. Fisher linear discrimination (1936) is a successful technique in supervised classification. It provides a linear rule which is simple, easy to implement, and with a clear interpretation. Furthermore, as it was pointed out by Hand (2006), linear rules are often very competitive against more sophisticated classifier technology. Let us suppose we observe a d-dimensional random vector in two populations. It is well-known that the key assumption on which linear discrimination relies is the homoscedasticity (i.e. that the class covariances of the vector in both populations are identical). If this fundamental assumption is not fulfilled (under heteroscedasticity), many other classifiers adopt a quadratic form. For example, this is the case of the classifiers obtained by the Mahalanobis distance or the Bayes rule when the measurements are normally distributed. We show that there are situations in which the covariances in the two populations are very different, and, however, a strictly quadratic classifier is ”almost” linear. This happens when the associated quadratic form is close to be a product of two hyperplanes. We find the exact condition under which this situation holds. The condition is related to the rank of certain matrices and allows us to compute explicitly the corresponding discriminant vector. The previous ideas make possible to generate hypothesis tests to check whether it is sensible to accept a linear classifier.

Pareto efficiency for the concave order and multivariate comonotonicity. Speaker: Guillaume Carlier, UniversitéParis Dauphine, France. Co-authors: Rose-Anne Dana, Alfred Galichon. In this talk, we will focus on efficient risk-sharing rules for the concave dominance order. For a univariate risk, it follows from a comonotone dominance principle, due to Landsberger and Meilijson, that efficiency is characterized by a comonotonicity condition. The goal of this paper is to generalize the comonotone dominance principle as well as the equivalence between efficiency and comonotonicity to the multi-dimensional case. The multivariate setting is more involved (in particular because there is no immediate extension of the notion of comonotonicity) and we address it using techniques from convex duality and optimal transportation.

Coherent multivariate risk measures and depth-trimming. Speaker: Ignacio Cascos, Universidad Carlos III de Madrid, Spain. Co-authors: Ilya Molchanov.

44 We model a risky portfolio as a random vector and assess its risk in terms of a convex set. In this framework, two (set-valued) risks are compared through the inclusion relation, i.e. we say that a vector portfolio X is less risky than another one Y , if the risk of X is contained in the risk of Y . Further, two risks can be aggregated through their Minkowski addition, and a kind of Minkowski subadditivity of these risks enables us to talk about coherent risks. For these (set-valued) multivariate risk measures, we obtain a duality result. Depth-trimmed regions constitute a well-known tool in multivariate statistics. They are sets of central points with respect to a multivariate probability distribution. We will see that a simple transformation turns them into risks and thus constitute an important source of risk measures.

Rare event simulation for a static distribution. Speaker: FrédéricCérou, INRIA Rennes - Bretagne Atlantique, France. Co-authors: P. Del Moral, T. Furon, A. Guyader. We will discuss the rare event simulation for a fixed probability law. The motivation comes from problems occurring in watermarking and fingerprinting of digital contents, which is a new application of rare event simulation techniques. We provide two versions of our algorithm, and discuss the convergence properties and implementation issues. A discussion on recent related works will also be provided. Finally, we will give some numerical results in watermarking context.

Detection of spatial clustering through grouping and average likelihood ratio test statistics. Speaker: Hock Peng Chan, National University of Singapore, Singapore. This talk consists of two parts. In the ﬁrst part we consider the use of false discovery rate (FDR) control in the analysis of spatial clustering. Because of the high correlation between neighboring scores, it is important that we ﬁrst group scores that are geographically close together and compute a p-value for each group. These group p-values are then compared using group FDR control. We show that there is a lower actual FDR compared to a direct application of FDR control on all the scores individually. In the second part of the talk, we consider various ways of computing group p-values. In average likelihood ratio (ALR) test statistics, we take the average of the likelihood ratios of all the scores in a group whereas for the spatial scan, we consider the maximum score. We show that the ALR test statistic computes p-values more easily and has a higher detection power than the spatial scan.

Branching processes in random walks. Speaker: Haiyan Chen, Jimei University, China. Branching processes and random walks are two historical topics in applied probability and they relate to each other closely. On the one hand, it is well known that a branching process can be naturally looked at as a random walk on the non-negative integers, so the knowledge on random walks can be used to study branching processes. For example, a general result for the total progeny of a branching process can be derived by using the Hiting Time Theorem for random walks. On the other hand, as early as 1975, Dwass showed that some branching processes arise naturally in random walks on the real line. Here we want to explore further the connections between the two subjects, though the emphasis is placed on ﬁnding branching processes in random walks, since there is little

45 work after Dwass along this line.

Two-dimensional variable window scan statistics for Poisson process. Speaker: Jie Chen, University of Massachusetts, USA. Co-authors: Joseph Glaz. In this article approximations and simulations for the distributions of the two-dimensional scan statistic are derived for both conditional and unconditional Poisson process. The minimum p-value statistic is derived to test the clustering of events on the two-dimensional rectangular area under the null hypothesis of randomness. Numerical results are presented to compare the power of these continuous variable win.

Monte Carlo methods on sensitivities estimation of American options. Speaker: Nan Chen, The Chinese University of Hong Kong, Hong Kong. Co-authors: Yanchu Liu. In this paper we investigate how to derive efficient Monte Carlo estimators to American option sensitivities. Derivative price sensitivities are important inputs in risk management. Whereas the prices themselves can often be observed in the market, their sensitivities cannot, so accurate calculation of sensitivities is an crucial issue in computational finance. A majority of traded equity options carry American-style terms; that is, the owner is allowed to exercise the option at her disposal. Such feature presents a challenge to Monte Carlo simulation. Without loss of generality, a wide class of American option pricing problems can be formulated by specifying an underlying price process St, 0 ≤ t ≤ T , a discounted payoff function H and a class of admissible stopping times T with values in [0,T ]. The option price is then the solution to the following optimal stopping problem

sup E[H(Sτ )]. τ∈T And the sensitivity estimation is to ﬁnd an unbiased estimator to

d θ sup E[H(Sτ )], (2) dθ τ∈T where θ is a parameter of interest. Thanks to the “smooth-pasting” property of the optimal exercise boundary of the American option (see, e.g. Peskir and Shiryaev (2006)), we manage to show that the order of diﬀerentiation and max is inter-exchangeable in (2), i.e., the sensitivity should be equal to

d θ sup E[H(Sτ )]. (3) τ∈T dθ Applying the pathwise derivative method and likelihood ratio method proposed by Broadie and Glasserman (1996), we can obtain efficient Monte Carlo estimators to (3). This method can be easily embedded in a variety of American option pricing algorithms, such as Longstaff and Schwartz (2001), Broadie and Glasserman (2004), Andersen and Broadie (2004) and so on. It does not require additional computational effort to yield the sensitivities. Extensive numerical experiments, including some high-dimensional cases, illustrate accuracy and efficiency of the method.

46 Processes of class Sigma, last passage times and drawdowns. Speaker: Patrick Cheridito, Princeton University, USA. Co-authors: Ashkan Nikeghbali, Eckhard Platen. We propose a general framework to study last passage times, suprema and drawdowns of a large class of stochastic processes. A central role in our approach is played by processes of class Sigma. After investigating convergence properties and a family of transformations that leave processes of class Sigma invariant, we provide three general representation results. The ﬁrst one allows one to recover a process of class Sigma from its ﬁnal value and the last time it visited the origin. In many situations this gives access to the distribution of the last time a stochastic process hit a certain level or was equal to its running maximum. It also leads to a formula recently discovered by Madan, Roynette and Yor expressing put option prices in terms of last passage times. Our second representation result is a stochastic integral representation of certain functionals of processes of class Sigma, and the third one gives a formula for their conditional expectations. From the latter one can deduce the laws of a variety of interesting random variables such as running maxima, drawdowns and maximum drawdowns of suitably stopped processes. As an application we discuss the pricing and hedging of options that depend on the running maximum of an underlying price process and are triggered when the underlying drops to a given level or alternatively, when the drawdown or relative drawdown of the underlying attains a given height.

Comparative analysis of space-time factoras, copulas, and BME methods in multivariate modeling. Speaker: George Christakos, San Diego State University, USA. The focus of this presentation is the comparative analysis of three diﬀerent methods to build multivariate probability models: (a) the factoras, (b) the copulas, and (c) the BME (Bayesian Maximum Entropy) methods. Factoras and copulas belong to the class of formal multivariate model building starting from the marginals, which includes models that are speculative and analytically tractable. Formal analogies between factoras and copulas are investigated in the composite space-time domain. Under certain conditions, factoras and copulas may be linked in terms of suitably chosen density weighting functions. The increased generality of factoras often comes at the cost of increased complexity. The BME method produces pdf models by integrating substantive knowledge (core and site-speciﬁc) and takes into account the contentual and contextual domain of the physical situation at hand.

Reinsurance and solvency. Speaker: M. MercèClaramunt, Universitat de Barcelona, Spain. Co-authors: Maite Mármol,Anna Castañer. This work is structured in two parts. In the first part we summarize the main results obtained on the effect of reinsurance strategies on the solvency measures of the insurer. In the second part we present a threshold proportional reinsurance strategy and we analyze the effect on ruin probability, time of ruin and deficit at ruin. This dynamic reinsurance strategy assumes a retention level that is not constant and depends on the level of the surplus. In a model with inter-occurrence times generalized Erlang(n)-distributed we obtain the integro-differential equation for the Gerber-Shiu function. Then, we present the solution for inter-occurrence times exponentially distributed

47 and claim amount phase-type(N). Some examples for exponential and phase-type(2) claim amount are presented.

Flowers and wedges as new tools for the stereology of particles. Speaker: Luis M. Cruz-Orive, Universidad de Cantabria, Spain. Recently (Cruz-Orive, 2005) a new decomposition has been found for the motion invariant density of straight 3 lines in R , with applications in stereology (Cruz-Orive, 2005; Cruz-Orive, Ramos-Herrera and Artacho-Pérula, 2010). The new decomposition leads to new rotational formulae which express the surface area and the volume of a bounded subset in terms of an observable functional defined in an isotropically oriented section (called a pivotal section) through a fixed point (called the pivotal point). The results have been extended to intrinsic volumes of manifolds in general space forms (Gual-Arnau and Cruz-Orive, 2009; Gual-Arnau, Cruz-Orive and NuñoBallesteros, 2010). A particular result reads: the surface area of a convex three dimensional subset equals four times the mean area of the support set of a pivotal section of the set. The mean is over isotropic rotations of the pivotal plane. The purpose of the talk is to present new exact computational details for this, and for a new formula for volume, when the subset is an arbitrary convex polyhedron. The results are applied to the grains of a cemented carbide previously analyzed by other methods (Karlsson and Cruz-Orive, 1997).

A random-projection based Gaussianity test for stationary process. Speaker: Juan A. Cuesta-Albertos , Universidad de Cantabria, Spain. Co-authors: Fabrice Gamboa, Alicia Nieto-Reyes. In this talk we present a procedure to test if a stationary process is Gaussian. The observation consists of a ﬁnite sample of a path of the process. The test is based on the fact (established in Cuesta-Albertos et al. (2007)) that, almost surely, a distribution is Gaussian if a randomly chosen one-dimensional projection is Gaus- sian, thus transforming the problem of testing the inﬁnite-dimensional Gaussianity in testing the Gaussianity of a one-dimensional distribution. Most of known tests only check if the one-dimensional marginals of the process under consideration are Gaussian, thus being at the nominal power against those non-Gaussian alternatives with Gaussian one-dimensional marginals. However, the procedure that we present here is consistent against every alternative (under some regularity conditions). The talk will also include some simulations and the analysis of some real data sets to compare our procedure with some other well-known tests proposed in the literature.

On uniform consistency in set estimation. Speaker: Antonio Cuevas, Universidad Autónomade Madrid, Spain. Co-authors: Ricardo Fraiman, Beatriz Pateiro-López. Set estimation is concerned with the problem of estimating an unknown set (typically the compact support of a distribution or a density level set) from a random sample of points. Obviously, the study of the consistency (in different versions) of the corresponding estimators is a subject of primary interest in this theory. This talk is devoted to the problem of uniform consistency (over appropriate classes) in set estimation. In the standard theory of asymptotic statistics, the uniform consistency issues are often tackled via the classical theory of empirical processes, including the well-known Vapnik-Cervonenkis combinatorial methodology. We analyze here a different approach by showing that some old results, due to Billingsley and Topsoe (1967, Z. Wahrs. Verw. Geb. 7, 1-16),

48 are particularly suitable for obtaining uniform consistency in set estimation. As speciﬁc applications we consider diﬀerent problems of support estimation under shape restrictions (convexity, star-shape, r-convexity) and plug-in estimation of density level sets.

Itôequation out of domino cellular automaton. Speaker: Zbigniew Czechowski, Polish Academy of Sciences, Poland. Co-authors: Mariusz Bialecki. The histogram method of reconstruction of the Itôequation from time series data was tested successfully in cases of time series generated by Itôequations only. However, for real, e.g. geophysical time series the following question arises: whether the complex phenomenon under investigation may be reliably described by the diffusive Markov process. Here, to give a partial answer, a simpler problem is considered; a natural phenomenon is modeled by a cellular automaton. The aim is to derive analytically, on the basis of automaton rules, the stochastic Itôequation and to compare the equation with that reconstructed by using the histogram method from time series data. To provide an analytical treatment, the domino cellular automaton with avalanches was constructed. Formulas concerning some exact relations for density, clusters, avalanches and other parameters in a quasi-equilibrium state were derived. It appears, however, that these formulas are approximately valid for some deviations from the equilibrium, so, the adequate Itôequation could be derived. Then, a comparison with simulations was also made and the results suggest a motive for the application of the procedure of construction of the Itôequation to natural time series. Hence, we conclude that Itôequations can be useful macroscopic models of phenomena in which microscopic interactions are averaged in an adequate way.

Stock valuation along a semi-Markov chain. Speaker: Guglielmo D’Amico, Universitàdegli Studi “G. d’Annunzio”, Italy. In this paper, a general dividend valuation model is provided assuming that the dividend growth rate is a discrete variable which is modelled by means of a semi-Markov chain. As a consequence, prices become duration dependent and consequently the financial market is no more efficient. The consideration of this more general valuation setting results in more complex solution procedures with respect to the Markov case or to the more simple case of independent random variables. In fact, a Markov chain model results in a simple linear system of equations. On the contrary the valuation procedure of the semi-Markov model requires the solution of a system of non-homogeneous first order linear difference equations with respect to the duration variable. Then, first of all, starting conditions corresponding to the case of no duration have to be determined by computing a series and second, the solution of the difference equation system leads to prices in correspondence of each possible duration time.

Two sided Markov-modulated reflection of Brownian motion. Applications to fluid queues. Speaker: Bernardo D’Auria, Universidad Carlos III de Madrid, Spain. Co-authors: Offer Kella. We present the analysis of the two-sided reflected Brownian motion for the case the two reflecting barriers depend on an external Markovian random environment. The process is interesting both from the theoretical point of view

49 and for its direct application to Brownian queues with modulated buﬀer size. For this process we show how to compute the stationary distribution and present some simple examples for the case of a ﬂuid queue in a two-state environment.

Minimax-Bayesian test for sequential testing of two composite hypothesis. Speaker: Boris Darkhovsky, Russian Academy of Sciences, Russia. The problem of sequential testing of two composite hypotheses is considered. Each of the hypotheses described by the density function depending on a parameter. The parameter belongs to one of two disjoint sets. The sequential procedure is proposed such that it minimizes the maximum over a family of prior parameter distribution Bayesian risk. The family of prior distributions consists of all probabilistic distributions on the parametric set such that the prior probability of one of the hypotheses is equal to a given number. It is proved that the procedure minimizes the greatest (over the parameter) average run length under the assumption of validity of any hypothesis among all sequential decision rules with given constraints on the greatest (over the parameter) error probabilities. The received results pass in classical Wald’s results for a case of simple hypotheses sequential testing problem.

Wiener disorder problem with observations at fixed discrete time epochs. Speaker: Savas Dayanik, Bilkent University, Turkey. Suppose that a Wiener process gains a known drift rate at some unobservable disorder time with some zero- modified exponential distribution. The process is observed only at known fixed discrete time epochs, which may not always be spaced in equal distances. The problem is to detect the disorder time as quickly as possible by an alarm which depends only on the observations of the Wiener process at those discrete time epochs. We show that Bayes optimal alarm times which minimize expected total cost of frequent false alarms and detection delay time always exist. Optimal alarms may in general sound between observation times and when the space-time process of the odds that disorder happened in the past hits a set with a nontrivial boundary.

Spacings ratio empirical processes. Speaker: Paul Deheuvels, UniversitéPierre et Marie Curie (Paris 6), France. We consider two independent samples of possibly unequal sizes, composed of independent and identically distributed random variables generated, respectively, by two continuous distribution functions. We are concerned with tests of the shift assumption that these distribution functions are identical, up to a shift parameter. For our needs, we construct an empirical process based upon ratios of spacings taken from each of these samples. Our main results show that this empirical process can be closely approximated, as the sample sizes increase to infinity, by sequences of Gaussian processes whose structure is fully characterized. As a consequence, we may build the tests of the shift assumption we have in mind with explicit asymptotic critical levels. The so-obtained approximating Gaussian processes have some interesting properties as well, which will be discussed in details. Part of this research is joint work with Gérard Derzko (Sanofi-Aventis, Monpellier).

50 Large graph limit for a SIR process in random network with heterogeneous connectivity. Speaker: Jean-StéphaneDhersin, UniversitéParis 13, France. We consider a SIR epidemic model propagating on a random network generated by a configuration model, where the degree distribution of the vertices is given and where the edges are randomly matched. The evolution of the epidemics is summed up into three measure-valued equations that describe the degrees of the susceptible individuals and the number of edges from an infectious or removed individual to the set of susceptibles. These three degree distributions are sufficient to describe the course of the disease. The limit in large population is investigated. As a corollary, this provides a rigorous proof of the equations obtained by Volz.

Universal generation of fractal statistics. Speaker: Iddo Eliazar, Holon Institute of Technology, Israel. Co-authors: Joseph Klafter. We present a stochastic superposition model which is capable of generating - in a universal fashion - various “fractal statistics”: anomalous diffusion, Levy laws, 1/f noises, and self-similarity. The model considers the superposition of independent stochastic processes: all processes sharing a common - yet arbitrary - stochastic process-pattern; each process having its own random parameters - initiation epoch, amplitude, and frequency. The stochastic superposition model is general and robust, and arises naturally in diverse fields of science and engineering: transmission channels and routers, and Internet servers in Communication; background noises in Physics and Electrical Engineering; probe dynamics in “stochastic baths”, and shot noise processes in Physics; river flows in Hydrology; tax revenues of states in Economics. In the context of Queueing Theory, the stochastic superposition model can be regarded as a generalized M/G/8 model, in which the superimposed processes represent the random workload processes of incoming jobs. Considering a specific process-statistic of the superposition model’s output, we focus on the following universality question: Is there a randomization of processes’ parameters which renders the output’s process-statistic invariant with respect to the processes’ common stochastic pattern? The answer - for various process-statistics - turns out to be affirmative, and yield the aforementioned “fractal statistics”. This research thus establishes a unified framework that: (i) explains the universal emergence of “fractal statistics” in diverse fields of science and engineering, and (ii) provides an explicit model and randomization-algorithms that universally yields desired “fractal statistics”. Observed from the “M/G/8 perspective”, this framework serves as natural and robust model for data-traffic processes displaying “fractal statistics” - which are prevalent in contem- porary communication systems.

Runs and scans in exchangeable trials with application to reliability. Speaker: Serkan Eryilmaz, Izmir University of Economics, Turkey. This talk is concerned with the exact distribution of runs and scans based on a sequence of exchangeable trials. Exact distributions of runs and scans are presented for both binary and multi-state exchangeable trials. Applica- tions and connections of the results related to the reliability of particular coherent systems are provided.

51 Optimal risk in marketing resource allocation. Speaker: Mercedes Esteban, University Carlos III of Madrid, Spain. Co-authors: Alejandro Balbás,JoséVidal. Marketing resource allocation is increasingly on the optimization of expected returns of investment. If the investment is implemented in a large number of repetitive and relatively independent decisions, it is acceptable method, but risk must be considered otherwise. The Markowitz classical mean/deviation approach to value marketing activities is of limited use when the probability distributions of the returns are asymmetric (usual in marketing). In this paper we consider an unifying treatment for optimal marketing resource allocation and valuation of marketing investments in risky markets where returns may be asymmetric, using coherent risk measures recently developed in finance. We propose a set of first order conditions for the solution and present a numerical algorithm for the computation of the optimal plan. We use this approach to design optimal advertisement investment instruments in sales response management.

Epidemic Detection using CUSUM. Speaker: Georgios Fellouris, Columbia University, USA. Co-authors: George V. Moustakides, Yajun Mei. We consider the problem of detecting a proportional change in the intensity of a counting process. We prove that if the counting process does not have explosions, the CUSUM detection rule is optimal in a Lorden sense. In particular, the CUSUM rule minimizes the worst-case conditional expected number of events that occur after the change and before the alarm given the worst possible history up to the time of the change. We discuss the consequences of this result to bio-surveillance applications such as the detection of epidemics. Finally, we suggest modiﬁcations of the optimal detection rule when the processes of interest are monitored in discrete times and not continuously.

Optimal portfolios and admissible strategies in Lévy-drivenmarkets. Speaker: JoséFigueroa-López, Purdue University, USA. Co-authors: Jin Ma. Motivated by the so-called shortfall risk minimization problem, we consider Merton’s portfolio optimization problem in a non-Markovian market driven by a Lévyprocess, with a bounded state-dependent utility function. Our approach is based on a multiplicative optional decomposition for nonnegative supermartingales due to Föllmer and Kramkov as well as a closure property for integrals with respect to a fixed Poisson random measure. Under certain constraints on the jumps of the price process, we characterize explicitly the admissible trading strategies and show that the dual solution is a risk-neutral local martingale.

On-line change detection and condition-based maintenance for a non-homogenous gamma process. Speaker: Mitra Fouladirad, Universit´ede Technologie de Troyes, France. Co-authors: Antoine Grall.

52 The aim of this paper is to propose an adequate condition-based maintenance policy to a gradually deteriorating system which deterioration trend can change suddenly. An on-line change detection algorithm is used to deal with the unknown abrupt change time. Consider a stochastically deteriorating system described by a scalar ageing variable which summarizes the condition of the system. The ageing variable increases with the system deterioration, and the failure occurs as soon as the system state crosses a known fixed threshold L called failure threshold. First, a homogenous gamma process with known parameters models the deterioration but, suddenly after an unknown time T the deterioration process changes and its evolution after T is modeled by a non-homogenous gamma process. The system is periodically inspected, and an on-line change detection algorithm estimates the abrupt change time. In order to avoid failure, a preventive replacement takes place if the system state exceeds an alarm threshold M, lower than L. At each inspection time the system can be replaced correctively or, preventively otherwise the decision is postponed until the next inspection. The value of M depends on the parameters of the deterioration process. In order to take into account the on-line available information on the mode of deterioration collected through monitoring the preventive threshold M has to be modified after T. The aim is to find the preventive thresholds, the inspection interval and the on-line change detection algorithm that lead to the lowest average maintenance cost.

Asymptotic analysis of a risk process with high dividend barrier. Speaker: Esther Frostig, University of Haifa, Israel. In this paper we study a risk model with constant high dividend barrier. We apply Keilson’s (1966) results on the asymptotic distribution of the time until occurrence of a rare event in regenerative process. We show that when the initial reserve is high, the asymptotic distribution of the time to ruin, and the amount of dividend until ruin are exponential. In the case that the initial reserve is small, we show that the time to ruin is a mixture of the exponential distribution and the distribution of the time to ruin in a risk process without barrier, given that ruin occurs. In this case the distribution of the amount of dividends is a mixture of exponential distribution and distribution degenerate at 0. We apply results from the theory of cycle maxima to obtain the parameters of the distributions.

Approximating the extreme right-hand tail probabilities for distributions of runs and patterns. Speaker: James C. Fu, University of Manitoba, Canada. Co-authors: Brad C. Johnson, Yung-Ming Chang.

The distribution of Xn(Λ), the number of a specified pattern Λ of length ` in a sequence of multi-state trials n {Xi}i=1, is vital important in statistical inference and applied probability. Fu and Johnson (2009) and Johnson and Fu (2010) introduced finite Markov chain imbedding approximation for the tail probability P (Xn(Λ) = k). They showed that for fixed k the ratio between exact and approximated probabilities tends to one as n → ∞, and also showed the finite Markov chain imbedding approximation performs much better than Normal and Poisson approximations. If k is a function of n and right hand probabilities are interested, then the finite Markov chain approximation performs less satisfactory and Normal and Poisson approximations perform extremely poor. This leads us to study the extreme right hand tail probabilities such as P (Xn(Λ) > n/` − k) and large deviation probabilities P (Xn(Λ) > kn). Theoretical and numerical results show that the proposed approximations perform

53 very well.

Sequential nonparametric estimation of the drift in diffusion based on discrete-time observations. Speaker: Leonid Galtchouk, Universitéde Strasbourg, France. Co-authors: Serge Pergamenshchikov. An adaptive sequential nonparametric procedure is constructed for estimating the drift coefficient in ergodic diffusion processes. A non asymptotic upper bound (an oracle inequality) is obtained for a quadratic risk. For this procedure the asymptotic efficiency is proved, i.e. the asymptotic quadratic risk of the constructed estimator coincides with the sharp lower bound for quadratic risks over all possible estimators which is the Pinsker constant.

Actuarial applications of epidemiological models. Speaker: JoséGarrido, Concordia University, Canada. Co-authors: Runhuan Feng. The risk of a global avian flu or influenza A (H1N1) pandemic, and the emergence of the worldwide SARS epidemic in 2002-03 have revived interest in the study of infectious diseases. Mathematical models are used in epidemiology to analyze the transmission dynamics and measure the effectiveness of controlling strategies. Works in the actuarial literature echo this epidemiological modeling, without any clear attempt to bridge these with actuarial applications. Here we define financial arrangements to cover the expenses resulting from the medical treatments of infectious diseases and study the actuarial implications. We illustrate a variety of numerical methods to calculate premiums and Reserves for these insurance products. For illustration purposes we analyze insurance products for the Great Plague in England and the SARS epidemic in Hong Kong.

Cross-covariance functions for multivariate random fields based on latent dimensions. Speaker: Marc Genton, Texas A&M University, USA. Co-authors: Tatiyana Apanasovich. The problem of constructing valid parametric cross-covariance functions is challenging. We propose a simple methodology, based on latent dimensions and existing covariance models for univariate random fields, to develop flexible, interpretable and computationally feasible classes of cross-covariance functions in closed form. We focus on spatio-temporal cross-covariance functions that can be nonseparable, asymmetric and can have different covariance structures, for instance different smoothness parameters, in each component. We discuss estimation of these models and perform a small simulation study to demonstrate our approach. We illustrate our methodology on a trivariate spatio-temporal pollution dataset from California and demonstrate that our cross-covariance performs better than other competing models.

Definition, characterization and usefulness of the extended truncated Tweedie-Poisson model. Speaker: Josep Ginebra, Universitat Politècnicade Catalunya, Spain. Co-authors: Jordi Valero, Josep Ginebra, Marta Pérez-Casany.

54 By truncating the sample space of the Tweedie-Poisson mixture model at zero, one can extend its parameter space. In the extended part of the parameter space the model is not the zero truncation of mixed Poisson distributions and, other than for a special case, it is not the mixture of zero truncated Poisson distributions either. This extended model proves to be useful by improving the ﬁt when data is more overdispersed than allowed by the unextended model, and by allowing for the use of the basic maximum likelihood based inference tools when the maximum likelihood estimate under the unextended model does not even exist.

Optimal dividend policy with different regulations and risk measures. Speaker: Silviu Glavan, Universidad Carlos III de Madrid, Spain. Co-authors: Alejandro Balbás. We consider a financial institution interested in consumption (dividends payment) in the next two years. The company has an initial amount to invest at time zero and can rebalance once a year. There are two optimal consumption decisions to be made in the first and the second year. An optimal dynamic portfolio selection rule is also involved. We discuss the problem above by considering different coherent and expectation bounded risk measures, as well as several accounting regimes. First of all, no accounting linked criteria are used (the “financial problem”), and several accounting standards are incorporated later. It is pointed out that the optimal set of decisions significantly depends on the assumed accounting regimes.

Scan statistics for i.i.d. normal random variables. Speaker: Joseph Glaz, University of Connecticut, USA. Co-authors: Joseph Naus, Xiao Wang. In this talk we present inequalities and approximations for the distribution, expected value and variance of the waiting time for a moving window of a ﬁxed length exceeding a speciﬁed threshold, for a sequence of i.i.d. normal observations. The cases of known and unknown mean and variance for the normal distribution are investigated. Numerical results will be presented to evaluate the performance of the inequalities and approximations that has been derived. Extensions to two and three dimensional problems will be discussed as well.

A weighted mean excess function approach to the estimation of Weibull-type tails. Speaker: Yuri Goegebeur, University of Southern Denmark, Denmark. Co-authors: Armelle Guillou. A new class of estimators for the Weibull-tail coefficient is proposed. For Weibull-type models the mean excess plot will show an ultimately linear behavior with a slope given by 1 − α, where α denotes the Weibull-tail coefficient, a property Dierckx et al. (2009) exploited to construct an estimator for α by applying a Hill-type operation on this ultimate linear part of the mean excess plot. This estimator will be incorporated in a larger class of estimators by considering linear combinations of log-spacings of the mean excess function evaluated at high levels. The asymptotic distribution of this new class of estimators is derived for an intermediate random threshold sequence, and under some mild conditions on the weight function and a second order condition on the tail behavior of the Weibull-type model. The finite sample properties of some estimators obtained with important

55 special cases of the weight function are examined with a small simulation experiment.

Semi-parametric probability weighted moments estimation revisited. Speaker: Mar´ıaIvette Gomes, Universidade de Lisboa, Portugal. Co-authors: Frederico Caeiro, BjörnVandewalle. For heavy-tailed models F and through the use of probability weighted moments based on the k largest observations in a sample of size n, either independent identically distributed or stationary and weakly dependent, we deal with the semi-parametric estimation of the Value-at-Risk at a level p, the size of the loss occurred with a small probability p = p(n), going to zero as the sample size n goes to infinity, as well as the dual problem of estimation of the probability of excedance of a high level x = x(n), going to infinity with n. Such estimation depends crucially on the estimation of the extreme value index, the primary parameter in Statistics of Extremes, which is also done on the basis of the same weighted moments. Under regular variation conditions on the right-tail 1 − F of the underlying distribution function F , we prove the consistency and asymptotic normality of these estimators, linking their asymptotic behavior to the asymptotic behavior of the extreme value index they are based on. The performance of these estimators for finite sample sizes is illustrated through a small-scale Monte-Carlo simulation and applications to real data in the fields of finance and insurance.

The crossover to the KPZ equation. Speaker: Ana Patricia Gon¸calves, Universidade do Minho, Portugal. Co-authors: Milton Jara. We consider the weakly asymmetric simple exclusion process to investigate the crossover regime for the density fluctuation field in the equilibrium setting. This crossover depends on the strength of the asymmetry which is given by an2−γ, where a and γ are positive constants. The crossover occurs when γ = 1/2, in such a way that if γ > 1/2 the limit density field is an Ornstein-Uhlenbeck process, while for γ = 1/2 the limit density field is a solution of the KPZ equation.

Bayesian estimation of degradation model defined by a Wiener process. Speaker: Fabrice Guerin, LASQUO - Universitéd’Angers, France. Co-authors: M. Barreau, S. Cloupet, J. Hersant. The constantly increasing market request of high quality vehicles ask the automotive manufacturers to perform lifetime testing in order to verify the reliability levels of new products. In this paper, we deal with two difficulties in reliability assessment for mechanical parts. On one hand, there is the small number of parts available for testing. On the other hand, there is the problem of wear. In the automotive applications, mechanical components subjected to relative motion of parts have to be designed against wear. In this paper, the Bayesian estimation of Wiener process parameters (usually used to define the degradation process) is studied to improve the estimation accuracy in incorporating the available knowledge on the product.

56 Bivariate splines for spatial functional regression and forecasting. Speaker: Serge Guillas, University College London, UK. Co-authors: Bree Ettinger, Ming-Jun Lai. We consider the functional linear regression models where the explanatory variable is a random surface and the response is a real random variable. Bivariate splines over triangulations represent the random surfaces. We use this representation to construct least squares estimators of the regression function and autoregressive estimators based on principal component analysis. We carry out an application of these two functional linear models to ozone concentration forecasting over the USA. In this paper, we report our numerical ﬁndings on the predictive skills of these two approaches using various triangulations. Furthermore, we compare our predictions with the ones obtained using thin-plate splines. Bivariate splines predictions outperform thin-plate splines ones and require less computational time. Finally, we quantify the variability in the predictions related to time sampling using the jackknife and report that bivariate splines predictions are better than the thin-plate splines ones in terms of uncertainties as well.

Robust-efficient test for exponentiality. Speaker: Jiqiang Guo, Iowa State University, USA. Goodness-of-fit tests based on either entropy estimation or empirical CDF have been used for testing the exponential distribution which is often used in studying lifetime and reliability. We present a weighted likelihood ratio goodness-of-fit test for exponentiality based on a combination of the Anderson-Darling test and a well-known entropy-based test. The new test can be readily used for completely observed data or Type II censored data. Simulation results indicate that the new test has robust power against a broad range of alternatives and outperforms either the CDF-based tests or the entropy-based tests in the alternatives examined. The usefulness of the new test is also demonstrated using real data sets.

On optimality gaps of asymptotically optimal policies in many-servers heavy-traffic. Speaker: Itai Gurvich, Northwestern University, USA. Co-authors: Baris Ata. Optimality gaps in many-server asymptotic optimality results are typically shown to be of a smaller order of magnitude than the square-root of the demand rate but a more refined characterization of these gaps is usually not provided. Our work is concerned with characterizing and improving these gaps. Specifically, we show how to modify the limiting diffusion control problem (and the resulting control) so as to improve on the optimality gap. The analysis relates the optimality gaps to the connection between preemptive and non-preemptive controls and between diffusion control problems and dynamic programming.

Iterative Monte Carlo for extreme quantiles and extreme probabilities. Speaker: Arnaud Guyader, Universit´ede Haute Bretagne - Rennes 2, France. Co-authors: N.W. Hengartner, E. Matzner-Lober.

d Let X be a d-dimensional random vector and Φ be a mapping from R to R. That mapping acts as a black

57 box, e.g., the result from some computer experiments for which no analytical expression is available. This paper presents an eﬃcient algorithm to estimate a tail probability given a quantile or a quantile given a tail probability. The algorithm improves upon existing multilevel splitting methods and can be analyzed using Poisson process tools that lead to exact description of the distribution of the estimated probabilities and quantiles. The performance of the algorithm is demonstrated in a problem related to digital watermarking.

Multi-dimensional quickest detection in coupled stochastic networks. Speaker: Olympia Hadjiliadis, University of New York, USA. Co-authors: Tobias Schaefer, H. Vincent Poor. This work considers the problem of quickest detection of signals in a coupled system of N sensors, which receive continuous sequential observations from the environment. It is assumed that the signals, which are modeled by a general processes, are coupled across sensors, but that their onset times may differ from sensor to sensor. Two main cases are considered; in the first one signal strengths are the same across sensors while in the second one they differ by a constant. The objective is the optimal detection of the first time at which any sensor in the system receives a signal. The problem is formulated as a stochastic optimization problem in which an extended minimal Kullback-Leibler divergence criterion is used as a measure of detection delay, with a constraint on the mean time to the first false alarm. The case in which the sensors employ cumulative sum (CUSUM) strategies is considered, and it is proved that the minimum of N CUSUMs is asymptotically optimal as the mean time between false alarms increases without bound. In particular, in the case of equal signal strengths across sensors, it is seen that the difference in detection delay of the N-CUSUM stopping rule and the unknown optimal stopping scheme tends to a constant related to the number of sensors as the mean time between false alarms increases without bound. While in the case of unequal signal strengths, it is seen that this difference tends to 0.

Fitting a 1-dependent model to stationary data with applications to scan statistics. Speaker: George Haiman, Universit´ede Lille 1, France. We present a quite general and easy to check condition on the joint distribution of two r.v.’s under which we construct a one parameter family of 1-dependent stationary sequences having this distribution for two consecutive r.v.’s. For discrete r.v.’s these 1-dependent sequences have interesting computational characteristics which make them somehow similar to Markov chains. We show that our method of estimating the distribution of 1-dimensional scan statistics presented in previous work may be extended to these sequences. We also show how this 1-dependent model can be used, as an easy to handle alternative to the Markovian model, to study several statistical characteristics of words and motifs of DNA sequences.

CLTs for Poisson hyperplane processes and extremal problems for convex bodies. Speaker: Lothar Heinrich, UniversitätAugsburg, Germany. In the first part of the talk we consider stationary Poisson processes of (d − 1)-dimensional hyperplanes in an d expanding sampling window %K, where K is some fixed convex body in R containing the origin as inner point. We derive two multivariate CLTs for the vector of the numbers of intersection k-flats (k = 0, 1, ..., d − 1) hitting %K as well as for the vector of their total k-volumes (k = 0, 1, ..., d − 1) within %K. We give a brief sketch of

58 the proofs which mainly rely on the asymptotic theory of U-statistics for random samples of random vectors. It turns out that due to the inherent long-range dependencies of the induced (non-Poisson) processes of intersection k-ﬂats (for k ≤ d − 2) the variances of the components grow faster than the d-volume of %K. In the second part we study the variance-covariance structure of the Gaussian limit vectors. In case of anisotropic hyperplane processes the asymptotic covariance matrices can be expressed in terms of the intrinsic volumes (or Minkowski functionals) of K and of the zonoid associated with the directional distribution. Finally, under the isotropy assumption, we discuss the problem of minimizing the limiting variances given the mean width of K. In particular, for the number of 0-ﬂats (= vertices of the corresponding hyperplane tessellation) this leads to new estimates of the dth-order chord power integral of K which slightly strengthen some classical inequalities of W. Blaschke as well as the isoperimetric inequality. These inequalities could be proved so far only in special cases and will be formulated as conjectures to be a challenge in future research.

Heat equation, first passage boundary problems and orthogonal polynomials. Speaker: Gerardo Hernández-del-Valle , Columbia University, USA. In this talk we will discuss applications of Hermite polynomials in the study of first passage time boundary problems and its relationship to the one-dimensional heat equation.

Structural invariance for a class of probability laws and a related branching particle system. Speaker: Kenneth Hochberg, Bar-Ilan University, Israel. Co-authors: Vladimir Vinogradov. We first describe the dynamics of a critical binary branching particle system (BPS), with and without spatial motion, and the related Dawson-Watanabe superprocess. We then study structural properties of some related probability distributions and delineate connections between them and the stochastic evolution of the BPS. For example, by considering the Athreya-Ney-type representation of the cluster structure of the particle system, we demonstrate that a Pólya-Aeppli sum of i.i.d.r.v.’s with a common zero-modified geometric distribution also follows a Pólya-Aeppli law. In contrast to other works in this field, we assume that the initial random number of particles follows a Pólya-Aeppli law, a condition that is consistent with stochastic models that emerge in such varied fields as population genetics, ecology, insurance risk, and bacteriophage growth. We resolve the issue of non-invariance of the initial field and manage to avoid related anomalies that arose in earlier studies. Also, we demonstrate that under natural additional assumptions, our particle system must have evolved from a scaled Poisson field starting at a specific time in the past. We also show that the corresponding high-density limit of our branching-diffusing particle system inherits an analogous backward-evolution property. Several of our results illustrate a general convergence theorem of Jørgensen et al. to members of the power-variance family of distributions.

Some limit theory for special classes of graphs. Speaker: Susan Holmes, Stanford University, USA. Co-authors: Persi Diaconis, Svante Janson. We study special cases of the limiting graph objects initially introduced by Lovasz, Szegedy, Borgs, Chase, Sos

59 and co-authors. These limits allow us to make statistical studies of graphs and in particular search for graphs with particularly simple underlying generative mechanisms.

Random walks on graphs using local degree information. Speaker: Satoshi Ikeda, Miyazaki University, Japan. Despite the lack of global topological information, both the hitting and the cover times for standard random walks on ﬁnite graphs can be bounded by O(n3). Hence a natural guess is whether a better transition matrix is designable if more topological information is available. In this talk we prove that the hitting (and hence the cover) time of a path graph is Omega(n2) for any transition probability matrix. Also, with a certain particular choice of the transition probability matrix that involves the degrees of the neighboring vertices of the current vertex, we show that for any graph G=(V,E) the hitting time is O(n2) and the cover time is O(n2 log n). These facts show that the degree information on the adjacent vertices is powerful enough for random walks to achieve the optimum hitting time.

A general multitype branching process with age, memory and population dependence. Speaker: Christine Jacob, INRA, France. We present a general class of multitype branching processes in discrete time with age, memory and population dependent individual transitions. Except in simple particular cases, the asymptotic behavior of this general process, as the time tends to infinity, is an open problem. So we instead study the behavior of limit models, as the initial population size tends to infinity, assuming that, at the initial time, either the types of interest are nonrare, or are rare. In the first case the limit model is a deterministic system on probabilities, and in the second case, the limit model is a multitype Bienaymé-Galton-Watson process on the rare types, with a Poissonian transition. The limit model in the first case allows to approximate the asymptotic behavior of the normalized process, and the one in the second case allows to calculate quantities such as the extinction time distribution and, in the subcritical case, the tree size distribution.

Estimating surface integrals on the boundary of unknown bodies: An application to Google Earth. Speaker: RaúlJiménez, Universidad Carlos III de Madrid, Spain. Co-authors: Joseph E. Yukich. The estimation of surface integrals on the boundary of an unknown body is a challenge for nonparametric methods in statistics, with powerful applications to physics and image analysis among other fields. Provided one can determine whether random shots hit the body, Cuevas et al. (Ann. Statist. 35:1031–1051) estimate the boundary measure (the boundary length for planar sets and the surface area for tridimensional objects) via consideration of shots at a box containing the body. The statistics considered by these authors, as well as those in subsequent papers, are based on the estimation of Minkowski content and depend on a smoothing parameter which must be carefully chosen. For the same sampling scheme, we introduce a new approach which bypasses this issue, providing strongly consistent estimators of both the boundary measure, together with the surface integral of scalar functions, provided one can collect the function values at the sample points. Examples arise in experiments in

60 which the density of the body can be measured by physical properties of the impacts or in situations where such quantities as temperature and humidity are observed by randomly distributed sensors. Our method is based on random Delaunay triangulations and involves a simple procedure for surface reconstruction from a dense cloud of points inside and outside the body. We obtain basic asymptotics of the estimator, perform simulations, and discuss via Google Earth’s data an application to the image analysis of the Aral Sea coast and its cliﬀs.

Approximating probabilities for runs and patterns in i.i.d. and Markov-dependent trials. Speaker: Brad C. Johnson, University of Manitoba, Canada. In this talk we will show that the number of non-overlapping occurrences of simple patterns in i.i.d. and Markov dependent sequences are always under-dispersed. This suggests that a binomial, rather than a Poisson approximation, may be better suited to these types of patterns, especially in the central limit domain. We will discuss such a binomial approximation and give a few examples of its application.

Max-stable random fields and negative-definite functions. Speaker: Zakhar Kabluchko, UniversitätUlm, Germany. Co-authors: Martin Schlather, Laurens de Haan. A random field is called max-stable if the maximum of any finite number of independent copies of this random field, taken pointwise, has the same distribution as the initial random field up to an affine transformation. Max- stable fields appear as limits of maxima of n i.i.d. random fields as n goes to infinity. In this talk we will be interested in a particular case of this setting: we will consider max-stable fields appearing as limits of maxima of independent (stationary or non-stationary) Gaussian fields. The class of limiting random fields will be completely described; it will be shown that this class is indexed by negative-definite kernels. The limiting random fields are related to a certain class of systems of “competing” particles. The starting positions of the particles are chosen according to a Poisson point process with intensity e−x, and then the particles move independently according to the law of a Gaussian process with stationary increments and some appropriate negative drift. The position of the “leading” particle in such a system as a function of time is a max-stable random field.

Ruin-probabilistic estimation of operational risk capital in finance and insurance. Speaker: Vladimir Kaishev, City University, UK. The paper presents a methodology for estimating operational risk capital in finance and insurance, based on operational risk measures incorporating ruin and the deficit at ruin, within a general risk model. It allows for inhomogeneous operational loss frequency (dependent inter-arrival times) and dependent loss severities which may have any joint discrete or continuous distribution. Under the proposed methodology, operational risk capital allocation is viewed not as a one off exercise, performed at some moment of time, but as dynamic reserving, following a certain risk capital accumulation function. The latter describes the accumulation of risk capital with time and may be any non-decreasing, positive real function h(t). Under these reasonably general assumptions, the finite horizon probability of non-ruin is explicitly expressed using closed form expressions, derived by Ignatov and Kaishev (2000, 2004, 2009) and Ignatov et al. (2001) and by setting it to a high enough preassigned value, say 0.99, it is possible to obtain not just a value for the capital charge but a (dynamic) risk capital accumulation strat-

61 egy, h(t). The latter approach has been proposed by Kaishev et al. (2008). These ideas are developed further by considering the joint distribution of the time to ruin and the deficit at ruin, as operational risk measure, alternative to the probability of finite-time ruin. For the purpose, an explicit expression for the joint probability that ruin will occur before time x and that the deficit at ruin will exceed a preassigned level, y is derived and it is demonstrated that, by setting it to a small enough value e.g., 0.01, a corresponding capital accumulation strategy, h(t) may be obtained. In view of its generality, the proposed methodology is capable of accommodating any (heavy tailed) distributions, such as the Generalized Pareto Distribution, the Lognormal distribution the g-and-h distribution and the GB2 distribution. Applying this methodology on numerical examples, we demonstrate that dependence in the loss severities may have a dramatic effect on the estimated risk capital. In addition, we show also that one and the same high enough survival probability may be achieved by different risk capital accumulation strategies one of which may possibly be preferable to accumulating capital just linearly, as has been assumed by Embrechts et al. (2004). The proposed methodology takes into account also the effect of insurance on operational losses, in which case it is proposed to take the probability of joint survival of the financial institution and the insurance provider as a joint operational risk measure. The risk capital allocation strategy is then obtained in such a way that the probability of joint survival is equal to a preassigned high enough value, say 99.9%.

Recent development of ordering conditional ordered data. Speaker: Baha-Eldin Khaledi, Razi University, Iran. Pn−1 Let n ∈ N, k ≥ 1, m1, ··· , mn−1 ∈ R, Mr = j=r mj, 1 ≤ r ≤ n − 1, be parameters such that γr = k + n − r + Mr ≥ 1 for all r ∈ {1, ··· , n − 1}, and let me = (m1, . . . , mn−1) if n ≥ 2 (m ˜ ∈ R arbitrary, if n = 1). The random vector (U(1,n,m,k˜ ), ··· ,U(n,n,m,k˜ )) with joint density function

n−1  n−1  Y Y mj k−1 h(u1, . . . , un) = k  γj  (1 − uj)  (1 − un) , j=1 j=1 deﬁned over the cone 0 ≤ u1 ≤ · · · ≤ un ≤ 1, is called the uniform generalized order statistics. Now, for a given distribution function F , the random vector

−1 −1 (X(1,n,m,k˜ ), ··· ,X(n,n,m,k˜ )) ≡ F (U(1,n,m,k˜ )), ··· ,F (U(n,n,m,k˜ )) is called the generalized order statistics (GOS’s) based on the distribution F . In this talk we review recent results on stochastic ordering among generalized order statistics and conditional generalized order statistics in one sample as well as two sample problems.

Multiplicative Kalman filter. Speaker: Mathieu Kessler, Universidad Politécnicade Cartagena, Spain. Co-authors: Valentine Genon-Catalot, Fabienne Comte. We study a non-linear hidden Markov model, where the process of interest is the absolute value of a discretely observed Ornstein-Uhlenbeck diffusion, which is observed after a multiplicative perturbation. We obtain explicit formulae for the recursive relations which link the relevant conditional distributions. As a consequence the predicted, filtered, and smoothed distributions for the hidden process can easily be computed. We illustrate the

62 behavior of these distributions on simulations.

Stochastic and deterministic population processes: From branching to the transport equation. Speaker: Marek Kimmel, Rice University, USA. A rather old controversy between stochastic and deterministic models of population growth and structure persists in mathematical biology literature. The deterministic approach advocates descriptions in the form of ordinary or partial (transport and/or diﬀusion) diﬀerential equations. On the other hand, applied probabilists developed approaches involving branching processes and their mathematical relatives. In the talk, it is demonstrated how a branching process with a continuous type space leads to a transport type result for expected values. The approach naturally leads to a mixed ODE/PDE system, when applied to a known hierarchical model of haematopoiesis. Merits of the probabilistic approach are discussed.

Some general results about transforming weighted discrete distributions. Speaker: CélestinC. Kokonendji, University of Franche-Comte, France. Co-authors: Marta Pérez-Casany. This work presents some properties related to weighted versions of a parametric count density in general and, in particular, related to weighted Poisson distributions. It is proved that to weight consecutively a count probability distribution with two different weight functions gives place to the same probability distribution, independtly of the order in which the weights are considered. Given that to left-truncate at zero, from now on to zero-truncate, a given count distribution is a particular case of weighted distribution, a consequence of this result is that to zero-truncate a weighted count distribution is equivalent to weight, with the same weight function, the zero- truncation of the initial distribution. This result is no longer true if one considers mixed distributions instead of weighted distributions as it has been proved by Böhningand Kuhnert (2006) for mixing distributions with finite support and in Valero et al. (2010) for mixed Poisson distributions in general. Two other consequences of the result presented are that the size-biased version and the zero-modified version of a weighted count distribution are equal, respectively, to the weighted version, with the same weight function, of the size-biased version and the zero-modified version of the initial distribution. From a practical point of view, these results are important for the practitioners because in cases where it is required to apply two or more types of weightening, they do not have to worry about the order in which the weights are considered.

Geometric ergodicity and the spectral gap of non-reversible Markov chains. Speaker: Ioannis Kontoyiannis, Athens University of Economics and Business, Greece. Co-authors: Sean P. Meyn. We argue that the spectral theory of non-reversible Markov chains may often be more effectively cast within the framework of the naturally associated weighted-L-infinity space instead of the usual Hilbert space L2. This observation is, in part, based on the following results. A discrete-time Markov chain with values in a general state space is geometrically ergodic if and only if its transition kernel admits a spectral gap in this weighted space. If the chain is reversible, the same equivalence holds in terms of L2, but in the absence of reversibility it fails: There are (necessarily non-reversible, geometrically ergodic) chains that admit a spectral gap in the weighted-L-infinity

63 space but not in L2. Moreover, if a chain admits a spectral gap in L2, then for any function in L2 there exists a corresponding Lyapunov function for the chain which dominates the original function, and the chain admits a spectral gap in the corresponding weighted-L-inﬁnity. The relationship between the size of the spectral gap, and the rate at which the chain converges to equilibrium is also brieﬂy discussed.

A survey on the pseudo-process driven by a high-order heat-type equation. Speaker: Aim´eLachal, Institut Camille Jordan, France. A survey on the pseudo-process driven by the high-order heat-type equation ∂/∂t = ±∂N /∂xN concerning the

first hitting times and sojourn times: fix an even integer N > 2 and let (Xt)t≥0 be the pseudo-process driven by N N the high-order heat-type equation ∂/∂t = ±∂ /∂x . The denomination “pseudo-process” means that (Xt)t≥0 is related to a signed measure (which is not a probability measure) with total mass equal to 1. For the pseudo- process (Xt)t≥0 started at 0, we consider the first overshooting times of a single barrier {a} or a double barrier {a, b}:

τa+ = inf{t ≥ 0 : Xt ≥ a} for a < 0, − τa = inf{t ≥ 0 : Xt ≤ a} for a < 0,

τab = inf{t ≥ 0 : Xt ∈/ [a, b]} for a < 0, as well as the sojourn times in the intervals [a, +∞), (−∞, a] and [a, b] up to a ﬁxed time T :

+ Ta = measure{t ∈ [0,T ]: Xt ≥ a}, − Ta = measure{t ∈ [0,T ]: Xt ≤ a},

Tab = measure{t ∈ [0,T ]: Xt ∈ [a, b]}.

± In this talk, we present some results and discuss some problems concerning the distributions of the times τa , τab, ± Ta , Tab.

Quickest sequential opportunity search in multichannel systems. Speaker: Lifeng Lai, University of Arkansas, USA. Co-authors: H. Vincent Poor, Yan Xin, Georgios Georgiadis. The problem of sequentially finding an independent and identically distributed (i.i.d.) sequence that is drawn from a probability distribution Q1 by searching over multiple sequences, some of which are drawn from Q1 and the others of which are drawn from a different distribution Q0, is considered. Within a Bayesian formulation, a sequential decision rule is derived that optimizes a tradeoff between the probability of false alarm and the number of samples needed for the decision. In the case in which one can observe one sequence at a time, surprisingly, it is shown that the cumulative sum (CUSUM) test, which is well-known to be optimal for a non-Bayesian statistical change-point detection formulation, is optimal for the problem under study. Specifically, the CUSUM test is run on the first sequence. If a reset event occurs in the CUSUM test, then the sequence under examination is abandoned and the rule switches to the next sequence. If the CUSUM test stops, then the rule declares that the sequence under examination when the test stops is generated by Q1. Expressions for the performance of the optimal sequential decision rule are also developed. The general case in which multiple sequences can be

64 examined simultaneously is also considered. The optimal solution for this general scenario is derived.

Making black boxes out of black boxes - the Bernoulli factory problem and its extensions. Speaker: Krzysztof Latuszynski, University of Warwick, UK. Co-authors: Ioannis Kosmidis, Omiros Papaspiliopoulos, Gareth O. Roberts, Dario Spano. Assume that a black box generating p-coins is available and 0 < p < 1 is unknown. Is it possible to use these p-coins and generate a min(1, 2p)-coin? Given a known function f, is it possible to obtain an f(p)-coin? The problem, known as the Bernoulli factory, in a simplified form originates from John von Neumann and naturally arises in exact algorithms for diffusions and in MCMC inference for diffusion parameter. I will present a reverse time martingale approach that offers a constructive solution and proceed to some generalizations and applications in diffusions inference.

Ruin probability in a homogeneous insurance risk model. Speaker: Claude Lefèvre, UniversitéLibre de Bruxelles, Belgium. This paper is concerned with an extended risk model for insurance. The claim arrival process is assumed to be homogeneous (in a specific sense), and the successive claim amounts are allowed to be dependent (to a certain extent). First, we investigate the dispersion and autocorrelation structures of the aggregate claims amount process. Then, we show how to evaluate, by simple recursive methods, the non-ruin probabilities over finite-time horizon.

Diffusion and cascading behavior in random networks. Speaker: Marc Lelarge, INRIA - ENS, France. We introduce a model of diffusion on graphs generalizing both the contact process and the bootstrap percolation where each node (not in the seed) is activated if the number of active nodes in a random subset of its neigh- borhood exceeds a random threshold. We study the final set of active nodes for a large random graph with a given degree sequence. Under some regularity conditions on the degree sequences, we show that the number of final active nodes satisfy a law of large numbers. We also consider the case of a seed with a single active node and give conditions under which it can trigger a large cascade, i.e. the final set of active nodes contains a non vanishing fraction of the size of the graph.

D2 statistics for word composition around replication origins of viral DNA. Speaker: Ming-Ying Leung, University of Texas at El Paso, USA. Co-authors: David SH Chew, Kwok-Pui Choi. Comparison of the similarities between two biological sequences is a major issue in computational biology, and S has traditionally been done using sequence alignment methods. The D2 statistic, and its variants (D2z, D2 & ∗ D2), however, rely upon on the comparison of the k-tuple content for both sequences. If two sequences are closely related, we would expect the k-tuple content of both sequences to be very similar. For a ﬁxed k, the

D2 statistics is deﬁned to be the inner product of the vectors of size k word counts in the two sequences under

65 consideration. An advantage of the D2 statistic is that it allows comparisons to be done quickly. In this paper, the D2 statistics and its variants are used to investigate the word composition around replication origins of viral DNAs, which are places on the DNA molecules where replication processes are initiated. We will show that the

D2 statistics will be smaller amongst replication origins than compared with other regions of viral DNAs. This suggests that D2 statistics can be used as an tool for the prediction of replication origins in viral DNAs.

Stochastic orders in network security. Speaker: Xiaohu Li, Xiamen University, China. Co-authors: Linxiong Li. Network science has attained rapid development during the past two decades. Since most work in this area rely heavily on experiments and simulations, it is urgent to develop nice models so as to gain insight on how the structure of a network has impact on the security issues. This talk introduces two stochastic models on certain networks, in which the famous k-out-of-n tolerant structure is ﬁrstly employed to characterize a node’s behavior. Based upon them, we draw the following two illuminating conclusions: (i) A P2P network with the node’s lifetime having more NWUE-ness is more resilient in the sense of having smaller isolation probability and longer durable time. (ii) The probability for the node of a vulnerable network to be compromised increases as the degree of the network grows in the increasing convex order. The two conclusions are consistent to what computer scientists have observed in either practical situations or experiment studies. Since the models proposed herewith greatly extend those in literature, the two theoretical results carry an insight on both designing a more secure system and enhancing the security of an existing system.

Nonparametric functional regression with functional responses using Gaussian process models. Speaker: Heng Lian, Nanyang Technological University, Singapore. Recently nonparametric functional model for functional responses has been proposed within the functional repro- ducing kernel Hilbert spaces (fRKHS) framework. Motivated by its superior performance and also its limitations, we propose a Gaussian process model whose posterior mode coincide with the fRKHS estimator. The Bayesian approach has several advantages compared to its predecessor. We also use the predictive process models adapted from the spatial statistics literature to overcome the computational limitations. Modifications of predictive process models are nevertheless critical in our context to obtain valid inferences. The numerical results presented demonstrate the effectiveness of the modifications.

Moment analysis of the Delaunay tessellation ﬁeld estimator. Speaker: Marie-Colette van Lieshout, CWI and Technische Universiteit Eindhoven, The Netherlands. Estimation of the intensity function of spatial point processes is a fundamental problem. In this talk, we shall use the Campbell-Mecke theorem to derive explicit expressions for the mean and variance of the Delaunay tessellation ﬁeld estimator recently introduced by Schaap and Van de Weygaert and compare it to the classic kernel estimators. Special attention will be paid to Poisson processes.

66 K-scan for anomaly detection. Speaker: Ji Meng Loh, AT&T-Labs Research, USA. Anomaly detection in disease surveillance often involves searching for clusters of unusually high incidence rates among current cases of disease incidence, against a background incidence rate which may be spatially varying due to underlying variation in population and environmental characteristics. We describe a K-scan method, to identify such anomalies, using components of the inhomogeneous K function. Specifically, we assign to each case i a value Ki. The sum of the Ki values over all case locations yields the overall inhomogeneous K function of the point pattern of disease locations. Clusters are identified using a bottom-up approach: high values of Ki are first identified and neighboring points are added iteratively to form candidate clusters. The inhomogeneous K function restricted to the region covered by each potential cluster is used as the criterion for selecting the reported cluster. Significance is computed using a parametric bootstrap approach with the inhomogeneous Poisson process. The intensity function is estimated using observations of case locations at prior time points. This intensity function is also used in the computations of the Ki values and provides a way to account for the spatially varying incidence rates when searching for clusters.

Stochastic modeling of portfolio experienced mortality: A co-integration based approach. Speaker: StéphaneLoisel, UniversitéLyon 1, France. Co-authors: Yahia Salhi. In this paper we propose a model that links the specific mortality of the policyholders of an insurance company with the corresponding national population mortality using an econometric model that captures the long-run relationship on the behavior of both mortality dynamics. This model does not lay the emphasis on the instantaneous correlation that the two given mortality dynamics would present but rather on the joint long-term behavior. The model captures additionally the short run relationship for the two considered mortality dynamics.

Ranking shape variability. Speaker: Miguel López-D´ıaz, Universidad de Oviedo, Spain. Co-authors: Carlos Carleos, M. ConcepciónLópez-D´ıaz. Shape analysis has a key role in many scientific fields. Loosely speaking, shape is considered as all geometrical properties which do not depend on location, scale and rotational effects. Shape variability is an important matter in shape analysis. As an example, the corneal endothelium is a layer of homogeneous, closely packed hexagonal cells which covers the interior surface of the cornea. It is well-known in ophthalmology that the more similar the endothelium cells are, the better health status the corneal endothelium has. A lesser variability in the shape analysis of the cells means a better health status of the endothelium. How is possible to rank endothelia in accor- dance with shape variability?. In this communication we introduce a stochastic order of shape variability of planar closed curves. For that purpose a special parametrization of such curves is introduced. Such a parametrization 2 generates a metric in an appropriate subclass of set of R . That metric will induce the measurability considered for the random magnitudes in the communication. The shape variability order is defined for such a kind of random elements. It is based on the comparison of the curvatures of the above parameterizations. Main properties of the order will be discussed, as those in relation to the preservation of the order under translations, orthogonal

67 transformations, contractions or weak convergence. An example of application will be discussed.

The idle period of the ﬁnite G/M queue with an interpretation in risk theory. Speaker: Andreas H. Lopker, Technische Universiteit Eindhoven and EURANDOM, The Netherlands. Co-authors: David Perry. We consider a G/M/1 queue with restricted accessibility in the sense that the maximal workload is bounded by

1. If the current workload Vt of the queue plus the service time of an arriving customer exceeds 1, only 1 − Vt of the service requirement is accepted. We are interested in the distribution of the idle period, which can be interpreted as the deﬁcit at ruin for a risk reserve process Rt in the compound Poisson risk model. For this risk process a special dividend strategy applies, where the insurance company pays out all the income whenever Rt reaches level 1. In the queueing context we further introduce a set-up time a ∈ [0, 1]. At the end of every idle period, an arriving customer has to wait for a time units until the server is ready to serve it.

Continuous, discrete and conditional scan statistics. Speaker: Wendy Lou, University of Toronto, Canada. Co-authors: James F. Fu, Tung-Lung Wu. The distributions for continuous, discrete and conditional discrete scan statistics are studied. The approach of finite Markov chain imbedding, which has been applied to random permutations as well as to runs and patterns, is extended to compute the distribution of the conditional discrete scan statistic, which is defined from a sequence of Bernoulli trials. It is shown that the distribution of the continuous scan statistic induced by a Poisson process defined on (0, 1] is a limiting distribution of weighted distributions of the conditional discrete scan statistics. A brief introduction to the approach and the main theorems will be presented. Numerical examples will also be provided to illustrate the theoretical results.

Probability bounds for model selection in ill posed inverse problems and active learning. Speaker: Carenne Ludeña, Instituto Venezolano de Investigaciones Cientif´ıcas,Venezuela. Co-authors: Ana Karina Ferm´ın. In this talk we discuss two problems related to supervised learning in the regression scenario. The first concerns estimation of ill posed inverse problems using general regularization methods. One of the most important issues in this setting is the adaptive choice of the regularization parameter. This can be achieved using an appropriate penalization procedure. Probability bounds for the supremum of the empirical process under the transformation which characterizes the regularization method yield the optimality of the procedure. The second, concerns the problem of active learning. That is, the adaptive choice of a labeling set. Traditionally this is achieved by fixing the model and choosing the label set by some optimization procedure, However recent interest has focused on simultaneous model selection and active learning. Typical methods include sequential algorithms although some batch procedures have been proposed also. The latter can be seen as a regularization procedure and the probability bounds discussed above can be used to study the properties of the estimator of the labeling set. Sequential methods can also be studied in this setting by using an additional random querying strategy. We study some

68 properties of the estimator in this case based on recent results in the classiﬁcation scenario.

Semi-Markov control processes with partially known holding times distribution. Speaker: Fernando Luque-Vásquez, Universidad de Sonora, México. Co-authors: J. Adolfo Minjárez-Sosa. We consider a class of semi-Markov control processes with Borel state and control spaces and possibly unbounded costs where the holding times distribution depends on an unknown and possibly non-observable parameter which may change from stage to stage. Our approach consists in supposing that the controller has an opponent, namely, the nature, which, at each decision epoch, once the controller choose his/her action, picks a parameter from a set which might depend on the current state and on the action selected. Then, the goal of the controller is to minimize the maximum cost incurred by the nature, that is, the controller must select actions guaranteeing the best performance in the worst possible situation. Thus, the system is modeled as a game against nature and we give conditions for the existence of minimax strategies, under the discounted and the average cost criteria.

A stochastic model of evolution. Speaker: FábioMachado, Universidade de Sao Paulo, Brazil. Co-authors: HervéGuiol, Rinaldo B. Schinazi. We propose a stochastic model for evolution. Births and deaths of species occur with constant probabilities. Each new species is associated with a fitness sampled from the uniform distribution on [0, 1]. Every time there is a death event then the type that is killed is the one with the smallest fitness. We show that there is a sharp phase transition when the birth probability is larger than the death probability. The set of species with fitness higher than a certain critical value approach an uniform distribution. On the other hand all the species with fitness less than the critical disappear after a finite (random) time.

Analysis of swaps in radix selection. Speaker: Hosam M. Mahmoud, The George Washington University, USA. Co-authors: Amr Elmasry. We study the number of swaps made by Radix Select (a one-sided version of Radix Sort) to find an element with a randomly selected rank. This kind of grand average provides a smoothing over all individual distributions for specific fixed order statistics. We give an exact analysis for the grand mean and an asymptotic analysis for the grand variance, obtained by poissonization, the Mellin transform, and depoissonization. The digital data model considered is the Ber(p). The distributions involved in the swaps experience a phase change between the biased cases p 6= 1/2 and the unbiased case p = 1/2. In the biased cases, the grand distribution for the number of swaps (when suitably scaled) converges to that of a perpetuity built from a two-point distribution. The tool for this proof is contraction in the Wasserstein metric space, and identifying the limit as the fixed-point solution of a distributional equation. In the unbiased case the same scaling for the number of swaps gives a limiting constant in probability.

69 A Monte Carlo semi-Markov backward model for a distributional claim reserve construction. Speaker: Raimondo Manca, Universitàdegli Studi di Roma “La Sapienza”, Italy. Co-authors: Fulvio Gismondi, Jacques Janssen. The claim reserving problem is currently one of the most debated in actuarial literature; (in the first issue of ASTIN 2009, 4 papers were on this topic). The high level of interest in this topic is due to the fact that Solvency II rules were approved in May 2009 and will come into operation in 2012. In that data the rule that establishes having the accumulated capital necessary to limit the risk failure fixed at 0.005 probability will be compulsory. For this reason the reconstruction of the claim reserve random variable distribution assumes a fundamental relevance. The aim of this paper is to present a method that is able to reconstruct the claim reserve distribution and that can take into account, in a natural way, the IBNyR (Issued But Not yet Reported) claims. The method is totally different from the models typically used in these problems given in the current literature. In the last part of the paper an applicative example constructed by tables that summarize 4 years of claims of an important Italian insurance company will be given.

Tail behaviour of β-ARCH processes. Speaker: Laszlo Markus, Eotvos Lorand University, Hungary. Co-authors: Peter Elek. The motto “light tails generate heavy tails”, is epitomised by the fact that even a Gaussian noise generates a stationary solution with regularly varying tail in the conventional quadratic ARCH model. The quadratic conditional variance is known to create similar tail behaviour under more general conditions, as well. However, in modelling environmental or some financial phenomena, there appears eventually a need to change the square to a 2β-power with 0 < β < 1, that is consider a β-ARCH-type process. The tail behaviour becomes then a subject to study. Being a little more general and allowing for asymmetry, we consider threshold β-ARCH models, driven by Weibull-type noises. Such a broad class of noises include e.g. the Gaussian and the double exponential ones as special cases. We show that the generated process has approximately Weibull like tail, too, albeit with different exponent: 1-β times that of the noise. We cannot, however, prove exact asymptotic tail behaviour only bound the tail from both sides by Weibull distributions of the same exponent but slightly different constants. The proof is based on taking an appropriate auxiliary sequence and then apply the general result of Klueppelberg and Lindner for the tail of infinite MA sequences.

Distributions of statistics over factor graphs. Speaker: Donald E. K. Martin, North Carolina State University, USA. Co-authors: John A.D. Aston. We compute exact distributions of statistics of variables whose joint distribution is represented by a factor graph. The graph can represent a Markov random ﬁeld, Bayesian network, or a conditional distribution given variables not represented in the graph (a conditional random ﬁeld). After giving a general formulation, we focus on conditional distributions of statistics over hidden state sequences given observed data. The methods discussed are relevant for graphs with a sparseness of edges that allows exact computation of the normalization constant. The distributions are obtained by combining the sum-product algorithm with a computation module that sequen-

70 tially updates the statistic’s value. We apply the methods to distributions associated with protein-protein and domain-domain interactions conditional on noisy protein-protein interaction indicators, and also to distributions of statistics related to CpG islands, conditional on DNA nucleotides.

Modeling and analysis of demographic data of Spain. Speaker: George Matalliotakis, Technical University of Crete, Greece. A modeling approach to Life Table Data sets is proposed. The method is based on a stochastic methodology and the derived first exit time probability density function. The Health State Function of a population is modeled as the mean value of the health states of the individuals. A new, simple model, based on a stochastic theory, introduced by Janssen and Skiadas, is presented and called S - model. The model proposed is compared to the three parameter Weibull and Gompertz models. The models will be applied to analyze the mortality data of Spain during the last century, focusing on the last 40 years. Furthermore the results will be presented and analyzed. The results indicate that the proposed model fits better to the data than the Weibull and Gompertz models. The methodology for the model building and the model proposed could be used in several cases in population studies in biology, ecology and in other fields.

Composite likelihood-based estimation methods for space-time stochastic processes. Speaker: Jorge Mateu, Universidad Jaume I de Castellón,Spain. We propose a weighted composite likelihood approach for the space and space-time covariance function estimation problem. In particular we present two estimation procedures: (a) maximization of a cut-off version of the composite likelihood, and (b) a solution of a weighted estimating equation coming from the composite likelihood. The weights are quite general and valid for any form of composite likelihood. They are obtained by minimizing a bound for the asymptotic variance of the composite likelihood. The proposed estimation methods can be considered as valid compromise between the computational burden of the maximum likelihood approach and the loss of efficiency of the classical weighted least squares approach using the empirical variogram. An identification criterion based on the weighted composite likelihood is also introduced. The effectiveness of the proposed procedures is illustrated through examples, simulation experiments and by reanalyzing a well known data set on Irish wind speed.

A coherence-based measure for spatial classification. Speaker: Jorge Mateu, Universidad Jaume I de Castellón,Spain. Co-authors: Aditya K. Mishra. The problem of detecting features of general shape in spatial point processes in the presence of substantial clutter is considered. Our goal is to remove clutter from images where one or several features are present and have to be detected. We derive a local version of the product density, called LISA, which is a second-order characteristic of spatial point processes. We then compute a coherence-based measure of spatial association between LISA functions using the concept of dynamic models based on Wiener filters. This measure needs the calculation of a power spectral density of the autocovariance of LISA functions and the corresponding cross-power spectral densities. We then develop a spatial classification method. This method can be applied without user input about

71 the number or shape of the regions. Our proposal is tested through simulated examples yielding high detection and low false-positive rates. Real case studies are also analyzed.

Undiscounted optimality criteria in economics and finance Speaker: Marco A. Méndez-Salazar, Universidad Veracruzana, México. Temporal discounting is typically associated to financial issues, while undiscounted performance indices are more often used in economic growth models. This paper deals with a discrete-time version of the classical Ramsey model, modified to take into account the effects of pollution of the environment on a social welfare index. Using dynamic programming techniques, optimal policies are found for both cases: the discounted welfare index and the (undiscounted) average welfare index. A comparison between optimal policies for these cases is presented.

Symmetries of probability distributions in view of applications to multiasset derivatives pricing. Speaker: Ilya Molchanov, UniversitätBern, Switzerland. Co-authors: Michael Schmutz. The put-call symmetry property says that for some asset price distributions the call with strike k and forward price F has the same value as the put with strike F and the forward price k. The talk first reminds the financial implications of this property, then explains how to describe it geometrically and extend it to the case of multiple assets. Then further symmetry properties of exchange options are discussed in view of applications to semi-static hedging of barrier options on multiple assets.

Partially sequential Lepage-Wolfe type test for a location-scale problem in environmental monitoring. Speaker: Amitava Mukherjee, Ume˚auniversitet, Sweden. A new nonparametric partially sequential test for a two sample general location-scale alternative is introduced. The proposed test is a combination of Wolfe type partially sequential test for location alternatives and the extended version of such a test for scale alternatives. We consider the idea of Lepage (1971) for combining two test statistics that are separately used to test location shift with or scale change. We consider a ﬁxed sample of size m from the control population. Our method of combination saves signiﬁcant amount of samples from test population when the null hypothesis of no change both in location and scale is violated. We discuss the asymptotic behaviour of the combined test statistic. We also carry out some simulation studies based on Monte-Carlo experiments. The results show extremely encouraging power performance. A small example based on real data is also included.

On two-stage comparisons with a control under heteroscedastic normal distributions. Speaker: Nitis Mukhopadhyay, University of Connecticut, USA. Co-authors: Tumulesh K. S. Solanky. New two-stage sampling methodologies are developed for both one-sided and two-sided comparisons between the means from treatment groups and a control. We suppose that we have ki(≥ 1) independent treatments with

72 th associated response variables Xi1, ..., Xiki , i = 1, ..., r(≥ 2). We let Xijl denote the l observation recorded in- 2 dependently and assume that their common distribution is N(µij, σi ), l = 1, ..., ni(≥ 2), j = 1, ..., ki, i = 1, ..., r. th Also, let X0l denote the l observation recorded independently from a control and we assume that their common 2 distribution is N(µ0, σ0), l = 1, ..., n0(≥ 2). The parameters µij’s, σi’s, µ0, and σ0 are assumed finite, unknown, and σi’s unequal, j = 1, ..., ki, i = 1, ..., r. Denote the treatment-control difference ∆ij = µij − µ0 and our goal is to make simultaneous one-sided and two-sided fixed-precision confidence statements regarding all ∆ij’s, j = 1, ..., ki, i = 1, ..., r. Specifically, given two preassigned numbers d(> 0) and 0 < α < 1, we develop two sets N N of appropriate two-stage stopping variables N0,N1, ..., Nr via procedures PI and PII respectively such that the N simultaneous probability that (XijNi − X0n0 ) − ∆ij ≤ d under PI and that (XijNi − X0n0 ) − ∆ij ≤ d under N PII would both exceed or equal 1−α for all j = 1, ..., ki, i = 1, ..., r..We note that the two-stage methodology for our one-sided problem covers more diverse applications than Dudewicz, Ramberg, and Chen’s (1975, Biometrische

Zeitschrift) methodology did since we no longer assume k1 = ... = kr = 1. With regard to our two-sided problem, no previous two-stage methodology was available in the literature. In this work, mathematical determinations of appropriate design constants with regard to either goal, the proposed methodologies, and the construction of the requisite tables are all new. The conference presentation will emphasize practical implementations of the proposed methodologies.

Expectiles as risk measures Speaker: Alfred M¨uller, Universit¨atSiegen, Germany. In this talk we consider expectiles as risk measures. Expectiles are a well-known concept in statistics, but seem to be hardly known in risk analysis. They are generalizations of the expectation in quite a similar fashion as quantiles (alias value at risk) are generalizations of the median. Thus it is quite natural to investigate their properties as risk measures. In this talk we show interesting properties of these risk measures, including coherence and their dual representation as worst case expectation. We also compare their properties to properties of other popular coherent risk measures like conditional value at risk.

New ordering results for coherent system lifetimes. Speaker: Jorge Navarro, Universidad de Murcia, Spain. We review some recent results on ordering properties of coherent systems. Many distribution-free ordering results are based on mixture representations obtained using signatures. We shall present the concept of stochastic prece- dence as a good alternative to compare coherent systems which are not ordered in the usual stochastic orders. We also show some ordering properties based on Gini index. These ordering results will be used to obtain bounds for the reliability and expected lifetime (or mean time to failure) of coherent systems with independently and identically distributed components having a common distribution with a given Gini index.

Scalable Bayesian event detection and visualization. Speaker: Daniel Neill, Carnegie Mellon University, USA. We present Fast Subset Sums (FSS), a new Bayesian method for fast and scalable event detection and visualization in multivariate space-time data. FSS extends the multivariate Bayesian scan statistic (MBSS), our recently

73 proposed Bayesian framework for multivariate event detection, to enable efficient detection and visualization of irregularly shaped clusters. FSS integrates prior information and observations from multiple data streams, computing the posterior probability of each type of event in each space-time region. This approach has many advantages over previous event detection approaches, including improved timeliness and accuracy of detection, and the ability to model and differentiate between multiple event types. Detected events can be visualized by displaying a “posterior probability map” showing the probability that each location has been affected. FSS enables detection and visualization of irregular clusters by defining a hierarchical prior over all subsets of locations. While a naive search over the exponentially many subsets would be computationally infeasible, we demonstrate that the posterior probability map can be efficiently computed, enabling rapid detection and visualization of emerging events. We compare the run time and detection power of FSS to our original MBSS approach (assuming a uniform prior over circular regions) on semi-synthetic outbreaks injected into real-world Emergency Department data from Allegheny County, Pennsylvania. We demonstrate substantial improvements in spatial accuracy and timeliness of detection, while maintaining the scalability and fast run time of the original MBSS method. This work was partially supported by NSF grants IIS-0916345, IIS-0911032, and IIS-0325581.

Sequential decision procedures in networks. Speaker: Igor Nikiforov, Universit´ede Technologie de Troyes, France. Co-authors: Lionel Fillatre, Igor Nikiforov, Guillaume Doyen, Gregory Bonnet. The goal of this paper is to propose a sequential change decision algorithm as a local motivation mechanism to optimize a global criterion in a large distributed system. Currently, the distributed systems are growing in size, complexity and dynamics. Hence, the management and control of large distributed systems can not be performed by a central unit anymore. Indeed, a central unit can not support such charges and acts as a single point of failure in the system. This paper is focused on an example of these systems, namely the peer-to-peer networks. Peer-to-peer networks are decentralized virtual networks in which each entity (called peer) takes on the role of both client and server. No centralized supervision exists. An important application is real-time content distribution that allows huge users communities to watch streaming content. Since peers continuously join and leave the network, service disruptions often occur. Hence, a CUSUM-type statistical sequential change decision procedure at the peer level is proposed to warrant the whole network stability. The proposed CUSUM-type algorithms are based on observed (at the peer level) stochastic processes like input-output traﬃc volumes and the distribution of watching session length. An adequacy between the virtual topology and the underlying physical one is used as a constraint which should be respected.

Variance risk premium, economic risks, and the cross-section of expected returns. Speaker: Alfonso Novales, Universidad Complutense de Madrid, Spain. Co-authors: Bel´enNieto, Gonzalo Rubio. This paper proposes the variance risk premium as a factor mimicking portfolio for hedging exposure to investment conditions in the ICAPM framework. We show that the excess return of the variance swap contract hedges equity market risks, interest rate and business cycle risks. However, the variance risk premium does not seem to explain the cross-sectional variation of average returns. Although there is a relatively important incremental explanatory power of the variance risk premium over and above the market risk factor, this result does no longer hold when

74 adding the Fama-French risk factors.

Large deviations and their applications to the problem of exit from a domain. Speaker: Adina Oprisan, Barry University, USA. Co-authors: Andrzej Korzeniowski. We study the eﬀect of small perturbations on large time intervals for a family of stochastic additive functionals of Markov processes switched by jump Markov processes. The averaged limit process evolves deterministically on random time intervals according to the transition times of a stationary jump Markov process. Small perturbations essentially inﬂuence the behavior of the system and asymptotics of probabilities of rare events play an important role in analyzing it. Large deviations is an asymptotic technique that provides a qualitative understanding of rare events. Using a week convergence approach, we establish a large deviation result and apply it to the problem of stability and the problem of exit from a domain of equilibrium. Explicit calculations are given for compound Poisson processes.

On some fractional point processes. Speaker: Enzo Orsingher, Universitàdegli Studi di Roma “La Sapienza”, Italy. In this work we consider the fractional version of the Poisson process, of the pure birth and pure death processes and also the fractionalisation of the linear birth and death process. The main idea underlying the fractional version of all these processes is to consider the difference-differential equations governing the state probabilities and replace them with the fractional derivative in the Caputo (or Dzhrbashyan–Caputo) sense. We are able to obtain the explicit probability laws for all processes considered in terms of Mittag–Leffler functions which generalise the classical distributions of the Poisson, pure birth (linear and non-homogeneous), pure death and also linear birth and death processes. Many detailed properties are investigated, including the renewal structure of the fractional Poisson processes and the moments of the population size of the models considered. The main tools of our analysis are represented by Laplace transforms of the generating probability functions which lead to special functions as the generalised Mittag–Leffler functions. All these processes are represented as compositions of their classical counterparts with a random time whose law is related to fractional diffusion equations. This representation offers a parallel method to reobtain the distributional properties of the processes derived by a combination of Laplace transforms with their inverses. Some applications are hinted and we show that a large panoply of processes is provided for modelling explosively expanding populations as happens in epidemics. The results presented here are published in Beghin and Orsingher (2009), Orsingher and Polito (a) (to appear in Bernoulli, 2010) and Orsingher and Polito (b) (to appear in Bernoulli, 2010).

Assessing the impact of autocorrelation in misleading signals in simultaneous residual schemes for the process mean and variance: numerical and stochastic ordering approaches. Speaker: Ant´onioPacheco, Universidade T´ecnicade Lisboa, Portugal. Co-authors: Patr´ıciaFerreira Ramos, Manuel Cabral Morais, Wolfgang Schmid. Misleading signals (MS) correspond to the misinterpretation of a shift in the process mean (variance) as a shift in the process variance (mean). MS occur when: the individual chart for the mean triggers a signal before the

75 one for the variance, even though the process mean is on-target and the variance is oﬀ-target; the individual chart for the variance triggers a signal before the one for the mean, although the variance is in-control and the process mean is out-of-control. MS can lead to a misdiagnose of assignable causes and to incorrect actions to bring the process back to target. Unsurprisingly, the performance assessment of simultaneous schemes for the process mean and variance requires not only the use of RL related performance measures, but also the probability of misleading signals (PMS). We assess the impact of autocorrelation on the PMS of simultaneous Shewhart and EWMA residual schemes for the mean and variance of stationary AR(1), AR(2) and ARMA(1,1) processes. This assessment is done numerically and also by means of stochastic ordering results.

Generalized Stirling permutations, families of increasing trees and urn models. Speaker: Alois Panholzer, Technische Universit¨atWien, Austria. Stirling permutations are a class of multipermutations introduced by Gessel and Stanley. We consider Stirling permutations and generalizations and establish bijective links between these combinatorial objects and certain families of increasing trees. In order to analyze the asymptotic behaviour of various parameters in generalized Stirling permutations we use these bijections, which allow then a description of the quantities via P´olya urn models. By analyzing these urn models we obtain limiting distribution results for the number of ascents, descents and plateux, the number of blocks, as well as the sizes of the blocks.

Portfolio optimization and multivariate Lévyprocesses. Speaker: Antonis Papapantoleon, QP Lab. and Technische UniversitätBerlin, Germany. In this talk we consider an investor who wants to choose the optimal portfolio from a pool of assets, subject to the initial capital (and possibly other constraints). The portfolio is optimized with respect to Conditional Value-at-Risk (CVaR). We will first describe the setup and discuss some numerical algorithms for the solution of the optimization problem. Another important problem is how to model the asset returns and their correlation and dependence structure. We will employ a factor model using Lévyprocesses as the driving motion. Lévyprocesses have become very popular in financial modeling because they combine flexibility with analytical tractability. We will compute the copula implied by the factor model and perform a sensitivity analysis. Then, we will turn our attention to the tail dependence coefficients, i.e. the asymptotic probability that two stocks crash together. This is of particular importance for the portfolio optimization problem, as CVaR is a coherent risk measure that is sensitive to tail risk.

Computational methods and algorithms in set estimation. Speaker: Beatriz Pateiro-López, Universidad de Santiago de Compostela, Spain. Within the context of set estimation, this work focuses on how practical analysis can be carried out. The development of computer methods and algorithms to efficiently implement set estimators is a major issue, closely related to the area of computational geometry. A well-studied example is the convex hull, a geometric structure of primary importance in set estimation that has many applications in pattern recognition and image processing, among others. There is an extensive literature detailing different algorithms that compute the convex hull of a set of points. In spite of its unquestionable relevance, the convex hull is not an appropriate estimator to effi-

76 ciently approximate non convex sets. For that reason, an eﬀort has been made in the last years to provide other geometrical constructions that achieve better results when estimating non convex sets. The α-convex hull and the α-shape have been shown to be successful approaches in this direction. The details of the implementation of these estimators are discussed in this work. Algorithms for the computation of these geometric structures start by computing the Voronoi diagram and Delaunay triangulation of the point set. These diagrams are classical mathematical objects whose implementation has also been largely studied. The library alphahull is the result of the implementation in R of the presented algorithms. This library is intended to provide a means of better understanding the nature of diﬀerent set estimators and their properties.

The M/G/1+G queue revisited. Speaker: David Perry, University of Haifa, Israel. We consider an M/G/1 queue with the following form of customer impatience: an arriving customer balks or reneges when its virtual waiting time, i.e., the amount of work seen upon arrival, is larger than a certain random patience time. We consider the number of customers in the system, the maximum workload during a busy period, and the length of a busy period. We also brieﬂy treat the analogous model in which any customer enters the system and leaves at the end of his patience time or at the end of his virtual sojourn time, whichever occurs ﬁrst.

Heavy-traffic limits via an averaging principle; convergence and stability. Speaker: Ohad Perry, Centrum Wiskunde & Informatica (CWI), The Netherlands. We consider a parallel-server system with two customer classes and two server pools operating under a Fixed- Queue-Ratio with Thresholds (FQR-T) routing rule. We prove a functional law of large numbers via an averaging principle and analyze properties of the limit, such as stability and interchange of limits. Building on the fluid limit we establish convergence to diffusion limits via state-space collapse.

A parametric semi-Markov model for the study of the mortality evolution. Speaker: Filippo Petroni, Universitàdegli Studi di Roma “La Sapienza”, Italy. Co-authors: Jacques Janssen, Raimondo Manca. Non-homogeneous Semi-Markov Processes (SMP) are a very powerful tool and in authors’ opinion can be used for the study of many real life phenomena. Despite this fact, this tool is not too much used in the applications. Instead, the applications of homogeneous SMP are numerous and they are done in many different fields. It is easy to understand that real world is a non-homogeneous environment and that the homogeneity hypotheses is a strong simplification. It is easy to understand that the construction of a “non-homogeneous non-parametric” model encounter difficulties for the huge number of data that are necessary for the evaluation of inputs. Anyway, if we get enough data we know what happened in the past but applied models are mainly useful for the forecasting of the future events. In non-homogeneous environment the past cannot be used directly for the evaluation of the future but it could be used to find the trend of the studied phenomenon. In this paper we present a parametric non-homogeneous model applied to the mortality forecasting problem. This is a typical non-homogeneous problem because, as well known, the mortality changes in function of the starting time. In the last part of the paper we will present an application of our non-homogeneous semi-Markov model to the Swedish data that we

77 got from HMD database.

A Bayesian hidden Markov model for software failures. Speaker: Antonio Pievatolo, Istituto di Matematica Applicata e Tecnologie Informatiche-CNR, Italy. Co-authors: Fabrizio Ruggeri, Refik Soyer. After reviewing briefly earlier work on imperfect debugging, we consider a model where, during the testing stages, the failure rate of the software is governed by a latent process. The state of the latent process reflects the effectiveness of the interventions, that is, the design changes, to the software after each observed failure time. We assume that the latent process is a Markov chain and that the failure times have an exponential distribution with rate depending on its state. The Bayesian estimation (by MCMC) of the state of the latent process is a straightforward matter, if the dimension of the state space is known. Then we consider also the problem of dimension selection as a Bayesian model selection problem, by showing how to calculate Bayes factors or running reversible jump MCMC for our specific model. We test our method on well known software failure datasets.

Finite time ruin probabilities for phase-type claims. Speaker: Konstadinos Politis, University of Piraeus, Greece. Co-authors: Esther Frostig, Susan M. Pitts. For the Sparre Andersen model of risk theory, we obtain a formula for the joint Laplace transform of the time to ruin, the number of claims until ruin and the deﬁcit at ruin when the claim amounts are phase type, and times between claim arrivals are i.i.d with general distribution. This extends a recent result of Borovkov and Dickson (2008). As an application of the main result, we obtain in particular and for special cases of the distributions of claim sizes and interclaim times, the exact distribution of the number of claims until ruin.

Maximum drawdown of a jump-diffusion process and pricing PIDE’s. Speaker: Libor Pospisil, Columbia University, USA. Maximum drawdown of an asset can be considered an indicator of a market crash. Thus, derivative contracts written on the maximum drawdown could serve as insurance against market crashes. In this talk, we assume that the price of the asset evolves according to a diffusion process plus a compound Poisson process. The question of interest is how to price contracts on the maximum drawdown in this jump-diffusion framework. Given the complexity of the underlying model, we argue that the most suitable method is to derive the pricing partial integro-differential equation and solve it numerically. The special feature of the equations is the presence of the running maximum and the running maximum drawdown, which may be discontinuous due to the jumps in the asset price. Moreover, the solution to the pricing equation may be discontinuous due to the possibility of jumps. We also discuss stability and convergence of the numerical method. Finally, we briefly address the problem of hedging these types of contracts.

78 Anticipated and adaptive prediction in functional discriminant analysis. Speaker: Cristian Preda, Universit´edes Sciences et Technologies de Lille, France. Co-authors: Gilbert Saporta, Mohamed Hedi Ben Hadj Mbarek. Linear discriminant analysis with binary response (Y ) is considered when the predictor is a functional random variable X = {Xt, t ∈ [0,T ]}, T ∈ R. Motivated by a food industry problem, we develop a methodology to ∗ ∗ ∗ ∗ anticipate the prediction of Y by determining the smallest T , T ≤ T , such that X = {Xt, t ∈ [0,T ]} and ∗ X provide similar predictions. The adaptive prediction determines for each new curve Xω the smallest T (ω), T ∗(ω) ≤ T , such that the prediction of Y using X observed only on [0,T ∗(ω)] is conserved at time T . For this purpose we deﬁne a conservation measure of the prediction with respect to the the prediction at time T .

Constrained control of continuous-time Markov chains. Speaker: TomásPrieto-Rumeau, Universidad Nacional de Educacióna Distancia, Spain. Co-authors: OnésimoHernández-Lerma. We deal with a continuous-time controlled Markov chain (CMC) with denumerable state space and possibly unbounded transition and reward rates. We are interested in discounted and average constrained optimality, that is, we want to maximize a discounted (resp. average) reward subject to a constraint on a discounted (resp. average) cost. We are concerned with the vanishing discount approach to average constrained optimality. More precisely, we give conditions ensuring that the average constrained optimal reward and policies can be obtained as the limit, as the discount rate vanishes, of the corresponding discounted constrained optimal reward and policies. This extends to average constrained CMCs the standard results on the vanishing discount approach for the average unconstrained case. We present an interesting counterexample for which the vanishing discount results for constrained problems do not hold. This example is shown to be related to a Slater-like condition for control problems.

Moment estimation for inhomogeneous spatial Cox processes. Speaker: Michaela Prokesova, Charles University, Checz Republic. In the paper we will discuss estimating procedures for inhomogeneous spatial Cox processes based on estimating equations and second order properties of the processes. These procedures are not yet fully developed in the literature, but definitely needed for the applications because of the unfeasibility of the maximum likelihood estimation for inhomogeneous Cox processes. The idea is to define a 2-step procedure, where in the first step the inhomogeneity part of the model is estimated from a first order estimating equation derived from the Poisson likelihood (thus ignoring the interactions in the model). In the second step conditionally on the estimated inhomogeneity the interaction parameters are estimated similarly like in the stationary case. Guan and Waagepetersen (2009) use the minimum contrast on the inhomogeneous K-function in the second step. We define two alternative methods using composite likelihood and so-called Palm likelihood. In the simulation studies these proved superior to the minimum contrast attitude.

79 Statistical inference for controlled multitype branching processes. Speaker: InésMar´ıadel Puerto, Universidad de Extremadura, Spain. Co-authors: Miguel González. Controlled multitype branching processes provide a useful way to model generation sizes in population dynamics studies where several types of individuals coexist and a control on the growth of population size is necessary at each generation. From a probabilistic viewpoint and in the framework of asymptotic linear growth of the expectation of the control variables, this model has been well studied. However the study of inference problems arising from this model has not been developed in deep. The purpose of this talk is to consider the estimation problem of the offspring mean matrix and consequently the estimation of its Perron–Forbenius eigenvalue, which is the threshold parameter for this model. To this end we make use of the weighted conditional least squares procedure. We also investigate the asymptotic behaviour of the proposed estimators.

Modelling the microstructure of foams using random tessellations. Speaker: Claudia Redenbach, UniversitätKaiserslautern, Germany. Macroscopic properties (e.g., permeability, thermal conductivity or acoustic absorption) of foams are highly influenced by the microstructure. Models from stochastic geometry are powerful tools for studying these relations. Edge systems of tessellation models are typically used to model open foams. We propose the use of random Laguerre tessellations which are weighted generalisations of the well-known Voronoi model. Using these models, a large variety of cell structures can be generated. Dilated versions of their cell edges then serve as models for the strut systems of open foams. A typical feature of real foams is a locally varying thickness of the struts. Usually, they are thicker at the vertices than at their centers. This structure is modeled using locally adaptable dilations of the edge system, where the size of the structuring element is chosen depending on the local structure. Finally, open foams are not necessarily perfectly open but may contain several closed facets. This feature can be modeled by including some of the tessellation facets into the foam model. Since the intensity and the orientation distribution of these facets have an impact on the macroscopic properties of the foam they have to be reproduced correctly in the model. We present a model capturing the aforementioned properties of real foams. Its application is discussed by some examples. The model fitting is based on geometric characteristics of the foams which are estimated from tomographic images of the materials.

Sum rules for hitting times of Markov chains. Speaker: JoséM. Renom, Universidad SimónBol´ıvar, Venezuela. Co-authors: JoséL. Palacios. Using matrix algebra we obtain a general equation for the sum, normalized with suitable constants, of all the expected hitting times in an ergodic Markov chain. This equation yields as corollaries, among others, Broder and Karlin’s formula, Foster’s formulas for electric networks and an expression of the Kirchhoff index in terms of the eigenvalues of the Laplacian.

80 Queues and risk models. Speaker: Jacques Resing, Technische Universiteit Eindhoven and EURANDOM, The Netherlands. Co-authors: Hansjoerg Albrecher, Sem Borst, Onno Boxma. There is a close connection between queueing and risk models. Globally speaking, this stems from the fact that in both cases the evolution of the system is determined by two discrete stochastic processes in similar, dual, ways. In the case of risk theory these are the interarrival times of the claims and the claim sizes, for queueing systems the interarrival times of the customers and the service requirements. In this talk we will focus on a risk model that describes the surplus of an insurance portfolio under the following additional assumption: tax payments are deducted from the premium income whenever the surplus process is at a running maximum. By linking queueing concepts with risk theory, we give, amongst other things, an insightful proof of the remarkably simple formula relating the survival probability of the process with tax to the corresponding probability in the model without tax. Queueing concepts we use are the maximum workload in a busy period of a single server queue on one hand, and residual service times of customers in an inﬁnite server queue on the other hand.

A vibrational shortcut to the mean ﬁrst passage time problem. Speaker: Shlomi Reuveni, Tel Aviv University, Israel. Co-authors: Rony Granek, Joseph Klafter. What is the average time a random walker takes to get from A to B on a fractal structure and how does this mean time scale with the size of the system and the distance between source and target? We take a non-probabilistic approach towards this problem and show how the solution is readily obtained using an analysis of thermal vibrations on fractals. Our result emphasizes the duality between diﬀusion and vibrations on fractal structures.

Stochastic ordering comparisons of sampling designs. Speaker: Yosef Rinott, The Hebrew University of Jerusalem, Israel, and LUISS, Italy. Co-authors: Larry Goldstein, Marco Scarsini. We compare estimators and sampling designs of the (essential) supremum and the integral of a function f defined on a measurable space when f(x) may be observed at a sample of x-points in its domain, possibly with error. Standard sampling theory compares estimators in terms of Mean Square Error, and it is known that the MSE reduces with increased levels of stratification. We study comparisons in terms of stochastic and convex ordering. We show, for example, that MSE order between different designs may hold while the more general convex ordering does not hold, and find conditions under which convex orders hold. Along the way we prove convex order inequalities that are of interest per se.

Pseudo-empirical likelihood inference for clusters of rare events. Speaker: Christian-Yann Robert, ENSAE, France. Events with low probability but disastrous impact are of particular interest to a large variety of applied sciences. The analysis of such rare events entails the understanding of the way in which they cluster in time. Especially it is very important to measure the strength of dependence between these events. We present a new statistical

81 methodology based on an empirical likelihood approach to estimate the distribution of the size of the clusters. Our results are illustrated through simulations and by applications to real data.

Exact posterior distributions over the segmentation space and model selection for multiple change-point detection problems. Speaker: StéphaneRobin, INRA/AgroParisTech, France. In segmentation problems, inference on change-point position and model selection are two difficult issues due to the discrete nature of change-points. In a Bayesian context, we derive exact, non-asymptotic, explicit and tractable formulae for the posterior distribution of variables such as the number of change-points or their positions. We also derive a new selection criterion that accounts for the reliability of the results. All these results are based on an efficient strategy to explore the whole segmentation space, which is very large. We illustrate our methodology on both simulated data and a comparative genomic hybridisation profile.

Forecasting macroseismic scenarios through anisotropic attenuation: A Bayesian approach. Speaker: Renata Rotondi, C.N.R. - Istituto di Matematica Applicata e Tecnologie Informatiche, Italy. The seismic hazard evaluation is heavily influenced by how the attenuation of the macroseismic intensity recorded at sites distant from the epicentre of a strong earthquake is modelled. This decay is generally assumed symmetric, because due to a point source, and calculated through loglinear regression relationships. In this work we aim at two objects: quantifying, by a binomial-beta probabilistic model, the uncertainty involved in the assessment of the intensity decay, an ordinal quantity often incorrectly treated as real variable, and, given the finite dimension of the fault, modelling non-symmetric decays but exploiting information collected from previous studies on symmetric cases. To this end we transform the plane so that the ellipse having the fault length as maximum axis is changed into a circle with fixed diameter. We start from an explorative analysis of a set of macroseismic fields representative of the Italian seismicity among which we identify three different decay trends by applying a hierarchical clustering method. Then we focus on the exam of the seismogenic area of Etna volcano where some fault structures are well recognizable as well as the anisotropic trend of the attenuation. As in volcanic zones the seismic attenuation is much quicker than in other zones, we first shrink and then transform the plane so that the decay becomes again symmetric. Following the Bayesian paradigm we update the model parameters and associate the estimated values of the intensity at site with the corresponding locations in the original plane. Backward validation and comparison with the deterministic law are also presented.

Stochastic enumeration method for rare-events, counting and combinatorial optimization. Speaker: Reuven Rubinstein, Israel Institute of Technology, Israel. We present a new method for rare-event probability estimation, counting and combinatorial optimization, called the stochastic enumeration (SE) method. In terms of counting, SE presents a stochastic replica of the naive full enumeration method. It is well known that the latter is typically meaningless since the associated counting sets, such as the sets of feasible solutions of the integer programming constraints, are huge. The SE method overcomes this difficulty by using a manageable sample size. We show how to implement the SE method for some well known difficult counting problems, such as self-avoiding walks and satisfiability problems, discuss its

82 convergence, and present numerical studies demonstrating its superiority to the classic splitting method.

Gibbs sampling methods for population processes in infinite dimensional models. Speaker: Matteo Ruggiero, Universitàdegli Studi di Pavia, Italy. We review some contributions to population genetics involving Gibbs sampling techniques. These are used to define countable representations of infinite dimensional diffusions on the simplex and of measure-valued processes with values on the space of Borel probability measures on some Polish space. The individual dynamics are specified discretely by means of Gibbs sampling algorithms applied to generalisations of Pòlya urn schemes, and then rescaled to yield the desired diffusion as limit in distribution. Special emphasis will be given to a particle process construction for the recent two-parameter extension of the infinitely-many-neutral-alleles model.

On optimal investment in a reinsurance context with a point process market model. Speaker: Wolfgang Runggaldier, Universitàdi Padova, Italy. Co-authors: Enrico Edoli. We study an insurance model where the risk can be controlled by reinsurance and investment in the financial market. We consider a finite planning horizon where the timing of the events, namely the arrivals of a claim and the change of the price of the underlying asset(s), corresponds to a Poisson point process. The objective is the maximization of the expected total utility and this leads to a nonstandard stochastic control problem with a possibly unbounded number of discrete random time points over the given finite planning horizon. Exploiting the contraction property of an appropriate dynamic programming operator, we obtain a value-iteration type algorithm to compute the optimal value and strategy and derive its speed of convergence. Following Schäl(2004) we consider also the specific case of exponential utility functions whereby negative values of the risk process are penalized thus combining features of ruin minimization and utility maximization. For this case we are able to derive an explicit solution.

Fear of loss, inframodularity, and transfers. Speaker: Marco Scarsini, Libera UniversitàInternazionale degli Studi Sociali Guido Carli di Roma, Italy. Co-authors: Alfred Mueller. There exist several characterizations of concavity for univariate functions. One of them states that a function is concave if and only if it has non-increasing differences. This definition provides a natural generalization of concavity for multivariate functions, which we call inframodularity. We define inframodular transfers and show that a finite lottery is preferred to another by all expected utility maximizers with an inframodular utility if and only if the first measure can be obtained from the second via a sequence of inframodular transfers. This result is a natural multivariate generalization of Rothschild and Stiglitz construction based on mean preserving spreads.

Stochastic comparisons of multivariate mixtures. Speaker: Moshe Shaked, University of Arizona, USA. We establish multivariate hazard rate, multivariate reverse hazard rate, and multivariate likelihood ratio stochastic

83 orderings among multivariate random mappings (mixtures) distributions. The new results streamline and simplify the proofs of some partial results that have recently appeared in the literature. Some applications in reliability theory and risk management may be described.

A probabilistic characterization for multivariate normality. Speaker: Yongzhao Shao, New York University, USA. Co-authors: Ming Zhou. Characterizing or learning about a multivariate distribution by examining linear combinations of lower dimensional components is a commonly used tool in statistics, machine learning, and pattern recognition. We present a new probabilistic characterization for multivariate normality of a random vector by examining normality of linear combinations of its components. In particular, we show that a random vector X has a p-variate normal distribution if and only if the following set has zero Lebesgue measure: U ∈ Rp : U 0U = 1 and U 0X is normally distributed.

Stochastic modeling and the first exit time problem. Speaker: Christos H. Skiadas, Technical University of Crete, Greece. Co-authors: Charilaos Skiadas. In this paper we explore the first exit time distribution function of a stochastic process crossing a linear or a curved boundary. The solution of the problem usually includes the solution of a stochastic differential equation to define a stochastic process and then to use this solution to find an exact or an approximate solution of the first exit time probability density function. We summarize the existing exact solutions for the first exit time problem and we also present several approximate solutions. A literature review is also included along with several illustrations from stochastic simulations of various stochastic processes, whereas characteristic graphs of first exit time distribution functions are given. Applications to various fields are mentioned and new or extended versions are discussed.

On the consistency of distorted variability measures with respect to dispersive orders. Speaker: Miguel Angel´ Sordo, Universidad de C´adiz,Spain. An important property of risk measures is consistency with respect to stochastic orders. In this work, we characterize two large classes of measures that quantify the notion of uncentainty in terms of the dispersive order (Bickel and Lehmann, 1979) and the weaker excess wealth order (Fern´andez-Ponce et al., 1998; Shaked and Shanthikumar, 1998). The classes under consideration include typical variabilty measures associated to distorted distributions and the results generalize those in (Sordo, 2009).

CLT for excursion sets of dependent random ﬁelds. Speaker: Evgeny Spodarev, Universit¨atUlm, Germany.

d Let X = {X(t), t ∈ R } be a quasi–associated, strictly stationary random ﬁeld such that X(0) has a bounded density. Assume that its covariance function is continuous satisfying some decay condition at inﬁnity. We study d excursion sets Au (X,T ) := {t ∈ T : X(t) ≥ u}, u ∈ R of X in a measurable set T ⊂ R over an arbitrary level

84 u and prove a central limit theorem (CLT) for their volume as T grows. It generalizes the corresponding CLT for stationary isotropic Gaussian random fields given in (Ivanov, A.V. et al., 1989). Moreover, a part of our work is devoted to an important special case of non–isotropic stationary Gaussian random fields. A statistical version of the CLT, a multivariate CLT for multiple levels uj, j = 1, . . . , m and corresponding statistical tests are provided as well. The proofs of our results are based on the CLT for (BL, θ)-dependent random fields given in (Bullinski, A.V. et al., 2007).

The drunken man and goodness-of-fit. Speaker: Michael Stephens, Simon Fraser University, Canada. In 1905, Karl Pearson asked for the distribution of the distance from the start, of a man who takes N steps of unit length in random directions. The problem has arisen again in recent work on testing fit to a distribution given a minimal sufficient statistic, and using the Rao-Blackwell distribution of the test statistic. When the test of fit is made, there is a remarkable correlation of the p-value with that given by the parametric bootstrap. The talk will begin with a discussion of Pearson’s problem, which has a fascinating history in its own right. In the goodness-of-fit problem, illustrated by testing the von Mises distribution, the Rao-Blackwell distribution will be estimated using the Gibbs sampler; mathematical details will be kept to a minimum and references given. Finally, the comparison with the bootstrap results will be shown, and some conclusions drawn.

Behaviour of change-point tests near the detection boundary. Speaker: Michael Stewart, University of Sydney, Australia. Certain elementary tests for a change point have a curious local power property: the test is either asymptotically perfect or asymptotically useless, depending on whether a certain parameter, when normalized by pn−1 log log n, has a limit greater than or less than 1. We present a boundary crossing result which sheds light on what happens when the corresponding limit equals 1, revealing that as with more standard parametric tests, all the action occurs on a scale of n−1/2.

Multivariate dispersion for random vectors having a common copula. Speaker: Alfonso Su´arez-Llorens, Universidad de C´adiz,Spain. For random vectors having a common copula some notions of multivariate dispersive orders are analyzed. In particular, we show that most of them can be characterized just for the comparison of the marginal distributions. In this context, we also analyze a condition for the variability ordering of increasing directionally transformations of the random vectors. For such a purpose, we focus our study on positive associated random vectors (PA). Finally, some examples and applications are studied.

Controlled diffusion processes and full cooperation in environmental topics. Speaker: Wojciech Szatzschneider, Universidad AnáhuacMéxicoNorte, Mexico. Failure of Copenhagen conference shows lack of agreements. Our proposal for environmental improvements uses the Principal-Agent Methodology, Nature being the principal, is represented by a financial institution that, if

85 created, will manage environmental funds. It is of primary importance to create mechanisms that will stimulate transfer of technologies. However, Permits-to-pollute and cap and trade just promote wild market and governmental interventions by assessing initial quotas. Good environmental solutions are: polluting less and reforesting. Apparent problems with P-A methodologies stem from the impossibility of precise modeling Nature. We can design reasonably well-in any state of nature- environmental certificates of improvements. We propose the emission of certificates that embrace large entities, and the fusion solution meaning that one part (agent) can make improvements in its counterpart. For pollution problems we analyze the case of GBM and compare this solution with standard collusive one for certificates: fund-temporal mean of square of X(t) + Y (t) in the case of full knowledge an agent has about the state of another (Bellman approach). The dual method is used for more general diffusions and certificates that depend on the final value only. It is unclear how to use this method more generally. If one agent is observing only its own domain, the optimal solution must go through direct calculations. The easiest model to analyze is the squared Bessel process with linear improvements. In this case we obtain precise results for different kind of certificates that stimulate cooperation going beyond standard Pitman & Yor calculations.

Minimax optimality of the Shiryaev-Roberts procedure. Speaker: Alexander Tartakovsky, University of Southern California, USA. Co-authors: Aleksey Polunchenko. Pollak (1985) proposed a randomized version of the Shiryaev-Roberts changepoint detection procedure where the zero initial condition was replaced with a random variable sampled from the quasi-stationary distribution of the Shiryaev-Roberts statistic. He proved that this “randomized” procedure has a very strong asymptotic optimality property - it minimizes the supremum conditional average delay to detection within the term of the order o(1) for a low false alarm rate when the average run length to false alarm approaches inﬁnity. The question whether Pollak’s procedure is strictly minimax for any false alarm rate has been open for two decades. We provide a counterexample, involving an exponential distribution, which shows that Pollak’s procedure is not optimal. We also show that a deterministically initialized Shiryaev-Roberts procedure, recently proposed by Moustakides, Pol- unchenko, and Tartakovsky (2009), that starts with a specially designed deterministic point is strictly minimax in this speciﬁc example.

Tracking a threshold crossing stopping time over a Gaussian random walk through noisy observations. Speaker: Aslan Tchamkerten, Telecom ParisTech, France. Co-authors: Marat V. Burnashev. We consider a particular setting of the tracking stopping time problem formulated by Niesen and Tchamkerten Pt in 2009. In our setting, there are two discrete-time correlated Gaussian random walks Xt = s · t + i=1 Vi and Pt Yt = Xt + ε i=1 Wi, where the Vi’s and Wi’s are independent standard normal random variables, and where s and ε are non-negative constants. Given the threshold crossing stopping time τa = inf{t ≥ 1 : Xt ≥ a}, a ≥ 0, the goal is to characterize minη E(|τ − η|), where the minimum is over all stopping times η with respect to the Y process. Our contribution consists of upper and lower bounds on E(|τ − η|) yielding

86 s r 2 ε2 1 min E(|τ − η|) = a (1 + o(1)) (a → ∞) . η π (1 + ε2) s3

Random geometric graphs for modelling the pore system of ﬁbre-based materials. Speaker: Ralf Thiedmann, Universit¨atUlm, Germany. Co-authors: Ingo Manke, Werner Lehnert, Volker Schmidt.

A stochastic network model is developed to describe the 3D morphology of the pore system in fibre-based materials. Such materials are used e.g. for the so-called gas diffusion layer (GDL) in polymeric fuel cells. In the pore space of GDL essential transport processes take place, like the diffusion of oxygen and hydrogen, respectively, towards the electrochemically active sites,or the drainage of produced water. Recently, various models for the solid phase of GDL, in particular for the fibre system itself, have been developed. In such models the pore space is considered as complementary set. However, this indirect description of pore space often leads to very complex geometric structures, i.e., it is described by huge sets of voxels, which make numerical simulations of transport processes quite complicated and computer time consuming, especially for large domains. In the present talk, a mathematical model for random geometric graphs is developed, representing the pore space directly. It can be applied e.g. to investigate transport processes in GDL on a large scale. We first model the vertex set of the graph by a stack of 2D point processes, which can physically be interpreted as pore centres. Each pore centre is then marked by its pore size. In the second step, the edge set of the graph is constructed, where the vertices are connected using tools from graph theory and MCMC simulation. The model parameters are statistically fitted to real 3D data gained by means of synchrotron tomography. Finally, the stochastic network model is validated by considering physical characteristics of GDL like their tortuosity, i.e., the distribution of shortest path lengths through the material relative to its thickness.

A hidden seasonal switching model for high resolution breakpoint rainfall data. Speaker: Peter Thomson, Statistics Research Associates Ltd., New Zealand. Co-authors: John Sansom.

A nonhomogeneous hidden semi-Markov model (NHSMM) for breakpoint rainfall data is proposed, which extends the homogeneous hidden semi-Markov model (HSMM) of Sansom and Thomson (2001) to incorporate stochastic seasonality. The NHSMM model is able to switch seasons at times that are earlier or later than the expected ones and, in this way, is able to explain additional seasonal variability due to varying length seasons. The model’s hidden rainfall states align with precipitation mechanisms that are seasonally invariant, but the state dynamics are assumed to vary with season. Recursions to construct the likelihood are developed and the EM algorithm used to fit the parameters of the model. An application of the model to breakpoint rainfall measurements from Invercargill, New Zealand, is discussed and the results of fitting a number of different NHSMMs are compared to those from fitting the non-seasonal homogeneous HSMM.

87 Kinetically constrained models: non-equilibrium coarsening dynamics. Speaker: Cristina Toninelli, Universit´esParis VI-VII and CNRS, France. Co-authors: Alessandra Faggionato, Fabio Martinelli, Cyril Roberto.

We study the dynamics of the East model, a unidimensional kinetically constrained model with Glauber dynamics in which birth/death of particles can occur only on sites which have an empty right neighbour. We consider the non equilibrium dynamics which occurs when we start at time zero from a configuration distributed with a Bernoulli measure with a density of empty sites different from the equilibrium density, q, and prove a series of conjectures previously proposed in physics literature. First we prove that when q goes to zero the dynamics is dominated by the coarsening of domains corresponding to completely filled intervals that are separated by two consecutive zeros. Furthermore, depending on the length of the domain, this coarsening occurs on very well separeted time scales. Indeed a domain can only disappear by merging with the neighbouring domain on the right and this occurs on time scales 1/qn for domains of size in 2n−1 + 1, 2n. As a consequence we prove that the probability that at time t a chosen site is occupied evolves by plateaus with changes occurring only at integer values of n(t) = logt/log(1/q). We also evaluate the asymptotic height of these plateaus which scales as a constant times 1/2n. Finally, we provide the asymptotic distribution for the length of domains and prove that their mean size coarsens as a power law of time with a non integer exponent which is proportional to the inverse of logarithm of q.

Stochastic properties of spacings based on order statistics. Speaker: Nuria Torrado, Universidad Carlos III de Madrid, Spain. Co-authors: Michael P. Wiper, Rosa E. Lillo.

Motivated in part by applications in reliability theory, life testing, and many applied areas, several authors have investigated the stochastic properties of order statistics and their spacings in the case when the observations are independent and identically distributed (i.i.d.). However, in some real situations, observations are non-i.i.d. Due to the complicated expression of the distribution in the non-i.i.d. case, only limited results are found in the literature. In this talk, we present stochastic properties involving spacings between order statistics from underlying heterogeneous distributions.

Ultimate ruin probability in discrete time with Bühlmanncredibility premium adjustments. Speaker: Julien Trufin, UniversitéCatholique de Louvain, Belgium. Co-authors: StéphaneLoisel.

In this talk, we consider a discrete-time ruin model where experience rating is taken into account. The main objective is to determine the behavior of the ultimate ruin probabilities for large initial capital in the case of light- tailed claim amounts. The logarithmic asymptotic behavior of the ultimate ruin probability is derived. Typical pathes leading to ruin are studied. An upper bound is derived on the ultimate ruin probability in some particular case. The inﬂuence of the number of data points taken into account is analyzed, and numerical illustrations support the theoretical ﬁndings. Finally, we investigate the heavy-tailed case. The impact of the number of data

88 points used for the premium calculation appears to be rather diﬀerent from the one in the light-tailed case.

Stochastic processes implementation methodology for life table data analysis of the population of Portugal. Speaker: Maria Vardoulaki, Technical University of Crete, Greece. Co-authors: Yiannis Dimotikalis, George Matalliotakis.

In this article we apply a methodology of stochastic processes to the life table data for the population of Portugal. The graphs (curves) formed by the mortality data of the population we have studied, are analyzed. We comment on their form and finally give important conclusions about the different mortality features of both sexes between male and female population. In addition, we refer to indicators concerning the increase in average life, the possible change in the number of births, deaths and immigrants. Furthermore, we mention the impact of the proposed model and the results obtained in the insurance science. Health status function is reported and estimated for the population too. The Health State Function H(t) is assumed to be at a specific level at the time of birth and then changes and gradually decreases to a zero level at the time of death. Then we use the life table data, apply the specific methodology of stochastic processes and compare to the models Weibull and Gompertz. The results of both models are displayed in graphs and compared. The study shows that the S-model gives lower errors, and describes the distribution with greater accuracy, than the Weibull and Gompertz models. The S-model is more appealing for Life Table Data sets analysis. It seems that the S-model differentiates itself from the Weibull and Gompertz in that the curve rises earlier than the Weibull and Gompertz curves.

Bayesian estimation of doubly stochastic Poisson processes for detection of seismicity phases. Speaker: Elisa Varini, Consiglio Nazionale delle Ricerche-IMATI, Italy. Co-authors: Ogata Yosihiko.

We aim to explore the hypothesis that the earthquakes of a seismic region occur under different physical conditions, corresponding to as many seismicity phases. As a consequence different occurrence rates are expected to be observed in a sufficiently long period. For this purpose we model seismic sequences by doubly stochastic Poisson processes. These processes belong to the family of the state-space models and are such that the observed process of the occurrence times of the earthquakes is a point process whose conditional intensity function is assumed to be dependent on both the past history and the current state. Many choices of the observed point process and of the hidden state process can be done. In particular we consider some point processes drawn from the literature on statistical seismology: the simple Poisson model and the epidemic-type aftershock-sequence model. Two modelling of the hidden state process are proposed and compared: a Markov process and a semi-Markov process. The former is a stationary process because the current state depends only on the last visited state; whereas the latter is non-stationary because the current state is assumed to depend on the past observations as well. Bayesian analysis of some real data sets is carried out: a sequential Monte Carlo method is applied to approximate the likelihood function and Markov Chain Monte Carlo methods are used for the parameter estimation.

89 General theory of the numeraire change for exotic options. Speaker: Jan Vecer, Columbia University, USA.

Exotic options are contracts on three or more underlying assets. For instance Asian options are contracts written on the money market, a stock, and the Asian forward; lookback options are contracts written on the money market, a stock, and an asset that represents the maximum price of the stock. In this talk we show that any of the underlying assets can be used as a reference asset for pricing of the exotic option, giving us at least three alternative price representations. In geometric Brownian motion model, the prices satisfy partial differential equations, and thus we also have at least three different pricing PDEs. We show that the alternative price representations are linked by a relationship known as the perspective mapping. We also explore different non-trivial symmetric relationships between various contracts.

The optimal method for pricing Bermudan options by simulation. Speaker: Carlos Velasco, Universidad Carlos III de Madrid, Spain. Co-authors: Alfredo Iba˜nez.

The Longstaff and Schwartz (2001) least-square method is the de facto method for pricing Bermudan options by simulation. An important, but overlooked, question is the optimal method for pricing Bermudan options. We address this question by deriving the cost function associated to suboptimal exercise. From the first order conditions of this minimization – the optimal estimator is a local least-square estimator, which is localized at the most significant part of the exercise boundary, and where only small value-matching errors (i.e., the difference between continuation and intrinsic values) are orthogonal to the regressors. This estimator can be implemented by parametrizing either the exercise boundary or the continuation value, where in the first (second) case we explicitly (implicitly) estimate the exercise boundary. The new method requires to iterate local regressions. We also show why a simple quadratic basis of functions works well in practice. The numerical examples confirm these results.

Bayesian quickest transient change detection. Speaker: Venugopal Veeravalli, University of Illinois at Urbana-Champaign, USA.

In the classical problem of quickest change detection, the change in the state of a system is modeled as a change in the distribution of an observation process which represents a noisy version of the state of the system. Also, the change is assumed to be persistent, i.e., the system is in state 0 (normal behavior) before the change and is in state 1 (abnormal behavior) forever after the change (until it is detected). However, in some applications, the change is transient and hence the state of the system goes back to 0, once the change disappears. For example, in intrusion detection applications, an intruder appears at a random time, stays for a random length of time in the system, and then leaves the system. The goal is to detect whether a change has occurred, even if the system has gone back to state 0 at the time of detection. In this transient change model, the distribution of the observations after the change disappears is the same as that when the change has not happened yet. Therefore, making a decision about the state of the system as being pre-intrusion or post-intrusion, based on the

90 observations, appears to be more challenging than in the case of persistent change. In this work, we pose the problem of quickest transient change detection as an optimal stopping problem. We obtain a Bayesian procedure that minimizes the expected detection delay subject to a constraint on the probability of false alarm. We also obtain a Bayesian procedure that maximizes the probability of stopping and declaring an alarm when the intrusion is present in the system, subject to a probability of false alarm constraint. In both of these procedures, when we stop, we distinguish between the hypotheses that the change has not disappeared yet and that the change has disappeared. For both procedures, we show that it is suﬃcient to keep only the a posteriori probabilities of change and post-change at any time.

A Lévyinput model with state-dependent services. Speaker: Maria Vlasiou, Technische Universiteit Eindhoven and EURANDOM, The Netherlands. Co-authors: Zbigniew Palmowski. (i) We consider a queuing model with the workload evolving between consecutive i.i.d. exponential timers {eq }i=1,2,... (i) according to a spectrally positive Lévyprocess Y (t) which is reflected at 0. When the exponential clock eq ends, the additional state-dependent service requirement modifies the workload so that the latter is equal to (i) (1) (i) Fi(Y (eq )) at epoch eq + ··· + eq for some random nonnegative i.i.d. functionals Fi. In particular, we focus + on the case when Fi(y) = (Bi − y) , where {Bi}i=1,2,... are i.i.d. nonnegative random variables. We analyse the steady-state workload distribution for this model.

Connection lengths in spatial stochastic networks: scaling limits and Monte Carlo methods. Speaker: Florian Voss, Universit¨atUlm, Germany. Co-authors: Catherine Gloaguen, Volker Schmidt.

We apply (marked) point processes on random geometric graphs and Palm calculus to model and analyze connection lengths in telecommunication networks. Using our modelling approach, we can take into account the infrastructure underlying the considered telecommunication network. In particular, we model this infrastructure by the edge set of some random tessellation and we represent network components by point processes on this edge set. Then we define the typical connection length between network components as a cost functional of this model. This typical connection length can be analyzed by Monte Carlo as well as asymptotic methods. More precisely, we show how the distribution of the typical connection length along the shortest path can be estimated using efficient simulation algorithms for the typical cell of random tessellations. Moreover, we present scaling limits for the distribution of the typical shortest path length for infinitely dense and sparse networks, respectively. In both considered scenarios, the limit is a simple parametric distribution whose parameters are known or depend only on the underlying tessellation model. Both methods are finally combined in order to compute parametric distributions for connection lengths in telecommunication networks. Furthermore, it is shown how these parametric distributions can be used to efficiently analyze existing and future telecommunication networks.

91 Blind fair routing in large-scale service systems. Speaker: Amy Ward, University of Southern California, USA. Co-authors: Mor Armony.

In a call center, arriving customers must be routed to available servers, and servers that have just become available must be scheduled to help waiting customers. These dynamic routing and scheduling decisions are very difficult, because customers have different needs, and servers have different skill levels. A further complication is that it is preferable that these decisions are made blindly; that is, they depend only on the system state and not on system parameter information such as call arrival rates and service speeds. This is because this information is generally not known with certainty. Ideally, a dynamic control policy for making routing and scheduling decisions balances customer and server needs, by keeping customer delays low, but still fairly dividing the workload amongst the various servers. We propose a blind dynamic control policy that routes according to a longest weighted idle server first rule, and schedules according to a generalized cl rule. We show that this policy is asymptotically optimal in the Halfin-Whitt many-server heavy traffic limit with respect to a finite time horizon problem that requires a fair division of idle time amongst servers be maintained at all times, and also performs well for a relaxed version of this problem that only requires that server fairness is achieved in the long run.

Suﬃx trees: A survey, and future challenges. Speaker: Mark Daniel Ward, Purdue University, USA.

Suffix trees are one of the most fundamental structures for data compression and pattern matching algorithms. They are retrieval trees (a.k.a. tries) built from the suffixes of a string (i.e., a data sequence). A rich combinatorial theory about overlapping strings has been known and utilized for three decades. Some of the combinatorial methods of analysis have been extended, to encompass suffix trees built over random strings whose distribution follows a Bernoulli model or a Markov model. Many opportunities exist for an extended, robust theory to much richer stochastic models that are applicable in practice, such as high-order Markov models and Hidden Markov Models. We will survey some recent results about suffix trees, derived by analytic, combinatorial, and probabilistic analysis in tandem. We will also outline some challenges for the future analysis of suffix trees and related structures.

Modelling extreme bursts above thresholds in a fractional stable toy model for natural complex systems. Speaker: Nicholas Watkins, British Antarctic Survey, UK. Co-authors: Sandra Chapman, Dan Credgington.

In 2 far-sighted contributions in the 1960s Mandelbrot showed the ubiquity of both non-Gaussian fluctuations and long-ranged temporal memory (the “Noah” and “Joseph” effects, respectively) in the natural and man-made worlds. Much subsequent work in complexity science has contributed to the physical underpinning of these effects, particularly in cases where complex interactions in a system cause a driven or random perturbation to be nonlinearly amplified in amplitude and/or spread out over a wide range of frequencies. In addition the modeling

92 of catastrophes has begun to incorporate the insights which these approaches have offered into the likelihood of extreme and long-lived fluctuations. In my talk I will briefly survey the research in Natural Complexity which the British Antarctic Survey mounted since 2005, in which the application of the above ideas in the earth system has been a key focus and motivation (e.g. Watkins & Freeman, Science, 2008; Edwards et al., Nature, 2007). I will then discuss in detail a standard toy model (linear fractional stable motion) which combines the Noah and Joseph effects in a controllable way, and discuss how it differs from the widely used continuous time random walk. I will describe how it is being used to explore the interplay of the above two effects in the distribution of bursts above thresholds (Watkins et al, PRE, 2009); and will conclude by exploring more recent work on multifractal models (Watkins et al, PRL Comment, 2009).

A Bayesian reliability model for repairable systems: An application to software data. Speaker: Michael Wiper, Universidad Carlos III de Madrid, Spain. Co-authors: Nuria Torrado, Rosa Lillo.

A commonly used deﬁnition of a repairable system (Ascher and Feingold, 1984) states that this is a system which, after failing to perform one or more of its functions satisfactorily, can be restored to fully satisfactory performance by any method other than replacement of the entire system. It is very obvious that most systems in the real world, such as automobiles, aircrafts or computers are designed to be repaired rather than replaced upon failure. The use of a Bayesian procedure allows the system reliability to be estimated by combining failure data of current stage with data of previous stages and prior information to be introduced into the inferential procedure. We present new models for the estimation of times between failures or numbers of failures in a given time. These models are non-parametric regression models based on Poisson failure counts and exponential inter-failure times, respectively. We construct a Bayesian inference method for our models using a Markov Chain Monte Carlo.

Pricing and hedging in aﬃne models with jump to default. Speaker: Alexander Wugalter, Princeton University, USA. Co-authors: Patrick Cheridito.

We analyze a general class of pricing models for European equity derivatives where the risk-neutral stock prices, interest rates and default of stock are jointly driven by an affine process. We extend the notion of a discounted moment generation function of the log stock price to the case when the underlying can default and show that it can be used for call option pricing using Carr-Madan’s method as well as for derivation of prices of power payoffs. Other European payoffs can be approximated using a mix of power payoffs and vanilla options. As we show the results are superior compared to using only power payoffs or only vanilla options. Moreover, within the class of such pricing models we determine those that are complete and discuss hedging by continuous trading in stock, corporate and government bonds as well as liquid vanilla options. The results are applied to the hedging of a variance swap. As a special case we consider Heston model with jump to default and stochastic interest rates.

93 Two-Stage Inference Methods for “Large p, Small n” Scenarios: Part I. Speaker: Kazuyoshi Yata, University of Tsukuba, Japan.

We propose effective methodologies to draw statistical inference from High Dimension, Low Sample Size (HDLSS) datasets. We first consider geometric representations of a HDLSS dataset. A HDLSS dataset has various types of characteristic of the geometric representation. For example, Hall et al. (2005, J. R. Statist. Soc.) showed that each data vector is approximately located on the vertices of a regular simplex in a high-dimensional space. With the help of the geometric representation, we give a variety of estimators for characteristics of a HDLSS dataset such as mean vectors, covariance matrices, eigenvalues, inverse covariance matrices, Mahalanobis distance, skew- ness, kurtosis, and so on. By using these estimators, we provide effective methodologies in statistical inference in HDLSS context. We construct a new type of confidence regions for a linear function of mean vectors. The linear function has a concentration of measure phenomenon in the HDLSS context. Therefore, the confidence region forms a sandwiched region between two high-dimensional spheres. We emphasize that a two-stage procedure, created in HDLSS context, is a strong tool to determine the sample size so as to construct such confidence regions having asymptotic consistency with a required accuracy. We demonstrate how the new estimation methodologies give a useful performance in HDLSS data situations by using a biological dataset. We further consider some problems of testing hypotheses for HDLSS data. We provide a two-stage test procedure that determines the sample size to control both a size and power so as to hold asymptotic consistency.

Weighted sums, stochastic orders, and entropy. Speaker: Yaming Yu, University of California - Irvine, USA.

Some stochastic inequalities are presented for weighted sums of i.i.d. random variables. The main inequalities are derived using majorization techniques under certain log-concavity assumptions. Related results comparing distributions according to Shannon entropy are also discussed.

Two-stage and sequential estimators of the normal variance. Speaker: Shelemyahu Zacks, Binghamton University, USA.

We consider two-stage and sequential estimation of the variance of a normal distribution. The paper derives the exact distributions of the corresponding stopping variables and in particular, the exact formulae of the bias and of the risk of the estimators at stopping. Exact numerical results are compared with simulations.

A ﬂuid EOQ model for perishable items with intermittent high and low demand rates. Speaker: Shelemyahu Zacks, Binghamton University, USA. Co-authors: Onno Boxma, David Perry.

We consider stochastic ﬂuid EOQ model, with intermittent periods of high demand and low demand rates. The inventory items are perishable, and have to be discarded after a speciﬁed period on the shelve. We assume that the high demand and the low demand periods follow an alternating renewal sequence, where the distribution

94 of the length of high demand period is exponential and that of the low demand is general. The inventory is replenished at the beginning of a cycle up to level q. We develop formulae for the distributions of a regenerative inventory cycle length, of the expected number of discarded items, the expected cost per inventory cycle, the long run average of holding cost, etc.

A binary inference framework for optimal channel selection in distributed sniﬀer networks. Speaker: Rong Zheng, University of Houston, USA. Co-authors: Gabriel Scalosub.

Independent component analysis (ICA) is a computational method for separating a multivariate signal into additive subcomponents supposing the mutual statistical independence of the non-Gaussian source signals. The classical Independent Components Analysis (ICA) framework usually assumes linear combinations of independent sources over the field of real-valued numbers. In this paper we model the observations of distributed sniffers as OR mixtures of binary independent users in the networks, and devise a binary inference framework to determine the active probability of users as well the adjacency matrix between users and sniffers. The inferred information is then utilized to decide the optimal channel allocation for sniffers by solving an integer program problem. We propose a constant-approximation ratio algorithm to the ILP. Simulation results show that the binary inference framework outperforms a binary adaption of linear ICA methods, and can achieve better coverage ratio using binary information only.

Statistical inference under spatial preferential sampling. Speaker: Zhengyuan Zhu, Iowa State University, USA.

Classical geostatistical methods implicitly assumes that the process of selecting the spatial sampling locations is independent of the spatial process observed at those locations. However, this assumption may not hold in applications such as mineral exploration and pollution monitoring, where the sampling rates depend on the spatial process being observed. Conventional inference methods can lead to deceiving results under such sampling designs which are referred to as preferential sampling. We propose a likelihood based approach which model the sampling process and the spatial process jointly. Eﬃcient algorithms are developed to ﬁt the model.

Thinning-stable point processes: New model in telecommunications. Speaker: Sergei Zuyev, Chalmers University of Technology, Sweden.

Point processes recently gained recognition in modelling different aspects of telecommunication systems: network components, mobile customers, infrastructure, etc. In many cases though the underlying system shows highly irregular spatial characteristics: number requests serviced by a web-server varies hugely as a function of popularity and happening events. Number of active mobile users calling during popular events: football match, rock concert differs in order of magnitudes from normal periods. This calls for development of point process models exhibiting such burst behaviour, in time or in space. We introduce a wide class of point processes which generally have infi-

95 nite expected number of points in a bounded domain, yet they appear unavoidably in the thinning-superposition of point processes schemes. We show that these processes are necessarily Cox processes driven by stable parameter measure and give insight into their cluster structure and further distributional properties.

Scaling limits for bandwidth sharing networks. Speaker: Bert Zwart, Centrum Wiskunde & Informatica, The Netherlands.

We consider a network with multiple classes of users, each class using a specific route. Each route requires a set of resources, and each user, as well as the network, operates under capacity constraints. Even under Markovian assumptions, this leads to models where the transition rates form the solution of convex programming problems. We therefore consider fluid and diffusion limits for such models.

96 Contributed Talks

Stochastic approximation in a M/G/1 queue with vacations. Speaker: Karim Abbas, Universit´ede Bejada, Algeria. Co-authors: Djamil Adssani. Many variants of M/G/1 system have been studied and applied extensively for performance evaluation purpose. An excellent survey of queueing systems with vacations, including some applications, was written by Doshi (1986, 1990). In this paper we discuss the applicability of the strong stability method (Adssani and Kartashov (1983), Kartashov (1996) and Abbas and Adssani (2010))to the M/G/1 queueing model with vacations. Our objective is to understand how the server’ vacations will aﬀect the system’s level of performance.

Bayesian and non-bayesian estimations of stress-strength reliability for Pareto distribution. Speaker: Abdallah Mohamed Abd-Elfattah, Cairo University, Egipt. Co-authors: M.D. Habib, H. Salm. This paper considers the estimation problem of the reliability of a system R in stress-strength model when the independent variable is distributed as Pareto distribution. We will discuss some diﬀerent methods for estimating the reliability, these methods are maximum likelihood, uniformly minimum variance unbiased, and Bayesian estimators based on conjugate and non-informative prior distributions. A comparison of the estimates obtained is performed. Interval estimators of the reliability are also discussed. Finally a numerical investigation will be carried out to study the properties of the new estimators.

Irreversible capacity expansion with proportional and fixed costs. Speaker: Hessah Al-Motairi, London School of Economics, UK. Co-authors: Mihail Zervos. We consider the problem of determining the optimal capacity expansion strategy that a firm operating within a random economic environment should adopt. We model market uncertainty by means of a geometric Brownian motion. The objective is to maximize a performance criterion that involves a Cobb-Douglas payoff function and associates a fixed and a proportional cost with each capacity increase. The resulting optimization problem takes the form of a two-dimensional impulse control problem that we explicitly solve.

Age and disability in Spain: An estimation using non-linear methods. Speaker: Pablo Alonso González, Universidad de Alcalá,Spain. Co-authors: Irene AlbarránLozano Irene, Juan Miguel Mar´ınDiazaraque. It is commonly assumed that the proportion of handicapped people grows with age. Namely, the elder the man/woman is, the more level of disability he/she suffers. However, the empirical evidence shows that this assessment is not always true, or at least, in the Spanish population. This study deals with the impact of age on disability in Spain. It is divided into three parts. The first one is focused in the state of arts about methods used in this paper. This section is emphasized on local regression, Neural Networks and Bayesian spline methods with

97 reversible jump (BARS). The second part of the work is focused in describing the way that disability is measured in this work. We use a former index defined by the first authors to distinguish between men and women. Finally, third section deals with the estimation of the parameters of the models. As different methods are used, there exist differences in results, not only among the methodologies but also between genders.

On the first passage theory and optimal control of spectrally negative jump-diffusions. Speaker: Florin Avram, Universite de Pau, France. We reexamine some classical first passage and optimal control problems in the light of recent progress on affine processes.

Time series segmentation by Cusum, AutoSLEX and AutoPARM methods. Speaker: Ana Laura Badagián, Universidad Carlos III de Madrid, Spain. Co-authors: Regina Kaiser, Daniel Peña. Time series segmentation has many applications in several disciplines as neurology, cardiology, speecg recognition, geology and others. Many series in these fields do not behave as stationary and the usual transformations to linearity can not be used. This paper describes and evaluates different methods for segmenting non-stationary time series. We propose a modification of the algorithm in Lee et al. (2003) which is designed to searching for a unique change in the parameters of a time series process, in order to find more than one change using an iterative procedure. We evaluate the performance of three approaches for segmenting time series: AutoSLEX (Ombao et al, 2002), AutoPARM (Davis et al, 2006) and the iterative cusum method mentioned above and referred as ICM. The evaluation of each methodology consists of two steps. First, we compute how many times each procedure fails in segmenting stationary processes properly. Second, we analyze the effect of different change patterns by counting how many times the corresponding methodology correctly segments a piecewise stationary process. ICM and AutoPARM present a very satisfactory behavior both for stationary and piecewise stationary processes. AutoSLEX is very sensitive to the way the partition are made. The performance of the three methods is illustrated with time series sets in neurology and speech.

Designing good deals in practice. Speaker: Raquel Balbás, Universidad Complutense de Madrid, Spain. Co-authors: Beatriz Balbás. We consider a general Asset Pricing Model and a non compatible Risk Measure, in the sense that sequences with unbounded risk and bounded price may be built. Interesting examples are the Black and Scholes model and the Conditional Value at Risk. The goal of the paper is the effective construction of such a sequence of strategies by using the properties of the probability space and the stochastic pricing process modeling the market evolution.

Modeling ozone pollution in Mexico city. Speaker: Juan M. Barrios, Universidad Nacional Aut´onomade Mexico, M´exico. Co-authors: Jorge A. Achcar, Eliane R. Rodrigues.

98 We will present a model to estimate the number of times the air quality standard is surpassed. We propose a non-homogeneous Poisson model to analyze this problem, i.e., the rate function at which the Poisson events occur is given and this is not constant as a function of time. This function will be dependent on some parameters that should be estimated. The parameter estimation is made using a Bayesian formulation based on a Markov Chain Monte Carlo sampling algorithm. We use data collected by the Mexico City’s monitoring network in order to apply the results presented. We also consider some historical considerations to propose better rate functions.

On point processes and random marked sets. Speaker: Viktor Benes, Charles University in Prague, Checz Republic. Co-authors: Marketa Zikmundova. In a recent paper Frcalova and Benes (2009) a Cox point process on a curve was studied. The driving intensity was considered on a bounded planar region, where a random curve was realized. The applications go to neuro- physiology (Frcalova et al. 2010), the curve being a track of an experimental animal and the events being spikes of a neuron in the animal’s brain. In the present talk the situation is described in the context of random marked sets (Ballani et al. 2009) and second-order characteristics are investigated. The assumption of a random-ﬁeld model from Frcalova and Benes (2009) is relaxed.

Semi-Markov risk migration models with initial and final backward: A case study. Speaker: Giuseppe Di Biase, Universitàdegli Studi “G. d’Annunzio”, Italy. Co-authors: Guglielmo D’Amico, Jacques Janssen, Raimondo Manca. At the moment, the problem of credit risk is one of the most important problems in the financial literature. It consists of computing the probability of an issuer and/or issue to make default on financial commitments. Inter- national organizations such as, Fitch, Moody’s and Standard and Poor’s, evaluate credit risk and give different ranks to issuers and issues. Clearly, the lower the rating the higher the interest rate that should be paid. This paper presents different models in order to analyze the rating evolution. All the models consider the backward time recurrence process to face the state duration time problem. In this way we can manage in a complete way the duration effects which represent one of the most important features in rating dynamics. For the first time we provide a credit risk application based on real data by considering initial and final backward times simultaneously. The models are implemented using Standard and Poor’s historical database.

Maximum likelihood inference for processes killed at a threshold. Speaker: Enrico Bibbona, Universit`adi Torino, Italy. Co-authors: Susanne Ditlevsen. We discuss how to make maximum likelihood estimates from one or more trajectories of a stochastic process which is observed at discrete times up to the moment it hits an absorbing boundary. Standard consistency arguments do not apply to such a case and we discuss possible extensions.

99 Central limit theorem and p-variations. Speaker: Hermine Biermé, UniversitéParis Descartes, France. Co-authors: Aline Bonami, JoséR. Leon. We consider p-variations of a stationary Gaussian sequence which admits a spectral density. Based on recent results of D. Nualart and S. Ortiz-Latorre (2008), and G. Peccati and C.A. Tudor (2004) and ergodic theorems, we obtain a central limit theorem according to a simple integrability condition on the spectral density. These results are then applied to harmonizable processes with a spectral density asymptotically equivalent to the fractional Brownian motion’ s one and improve significantly previous results (cf. H. Bierméand F.Richard, 2008).

Robust methods in semiparametric estimation with missing responses. Speaker: Graciela Boente, Universidad de Buenos Aires and CONICET, Argentina. Co-authors: Ana Bianco, Wenceslao Gonzalez-Manteiga, Ana Perez-Gonzalez. Most of the statistical methods in nonparametric regression are designed for complete data sets and problems arise when missing observations are present which is a common situation in biomedical or socioeconomic studies, for example. Classic examples are found in the field of social sciences with the problem of non-response in sample surveys, in Physics, in Genetics, among others. We will consider inference with an incomplete data set where the responses satisfy a semiparametric partly linear regression model and we will introduce a family of robust procedures to estimate the regression parameter as well as the marginal location of the responses, when there are missing observations in the response variable, but the covariates are totally observed. In this context, it is necessary to require some conditions regarding the loss of an observation. We model the aforementioned loss assuming that the data are missing at random, i.e, the probability of observing a missing data is independent of the response variable, and it only depends on the covariate. Our proposal is based on a robust profile likelihood approach adapted to the presence of missing data. We derive the asymptotic behavior of the robust estimators for the regression parameter and of a weighted simplified location estimator. For the latter, the asymptotic distribution is derived when the missing probability is known and also when it is estimated. A Monte Carlo study is carried out to compare the performance of the robust proposed estimators among them and also with the classical ones, in normal and contaminated samples, under different missing data models.

On boundary crossing probabilities for diffusion processes. Speaker: Konstantin Borovkov, The University of Melbourne, Australia. Co-authors: Andrew Downes. Computing the probability for a given diffusion process to stay under a particular boundary is crucial in many important applications including pricing financial barrier options. It is a rather tedious task that, in the general case, requires the use of some approximation methodology. One possible approach to this problem is to approximate given (general curvilinear) boundaries with some other boundaries of a form enabling one to relatively easily compute the boundary crossing probability. We discuss results on the accuracy of such approximations for both the Brownian motion process and general time-homogeneous diffusions and also some contiguous topics.

100 Extended dependency tree-HMM for non-rectangular sub-image modeling. Speaker: Mohamed El Yazid Boudaren, EMP School, Algeria. Co-authors: Abdel Bela¨ıd. Pixel-wise approaches for image classification are usually not suitable to solve problems often encountered in remote sensing applications. They result in a disgusting salt and pepper effect. To overcome the drawback of such approaches, more elaborated methods classify each pixel by taking into account some of its neighboring pixels, usually by computing a similarity measure (likelihood probability for instance). In most cases, this computation concerns pixels contained in square windows centered at the pixel to classify. However, in some stochastic image modeling frameworks, one may have to evaluate likelihood probabilities on non-rectangular windows, like in M. E. Y. Boudaren and A. Bela¨ıd(2009). In this work, we propose to extend the so-called dependency tree-hidden Markov model (DT-HMM) proposed in B. Merialdo (2005) to make possible such computation by allowing the four directional interactions between neighboring pixels instead of just two. This allows one to approximate the genuine 2D-HMM likelihood probability of observing the data contained in circular-like shaped windows or image blocks while maintaining the linear complexity of the traditional 1D-HMM. It was proven in some previous research works by B. Merialdo (2006) that the average value of the likelihood probability computed according to a relatively small number of random dependency trees constitutes a good estimation of the authentic likelihood probability. To validate our theoretical formalism, we show some results obtained in M. E. Y. Boudaren and A. Bela¨ıd(2010) where we propose a new scheme for land cover classification from high resolution aerial images.

Long runs from a conditioned random walk and importance sampling algorithm for rare event simulation. Speaker: Michel Broniatowski, LSTA UniversitéParis 6, France. In this talk we explore the asymptotic distribution of a random walk conditioned on its final value as the number of summands increases and we present an explicit algorithm for its simulation, with some application to rare event n simulation. Denote X1 := (X1, .., Xn) a set of n independent copies of a centered real random variable X with n k density p on R and S1 := X1+..+Xn. We consider approximations of the density of the vector X1= (X1, .., Xk) k n on R when S1 = nan and an is either fixed larger than EX or tends slowly to EX from above. The value of k may depend on n and satisfies 0 ≤ lim sup k/n ≤ 1 n→∞ together with lim n − k = ∞. n→∞ Therefore we may we consider the asymptotic behavior of the density of the trajectory of the random walk on long n n runs. For sake of applications we also address the case when S1 is substituted by T1 := f (X1) + ... + f (Xn) for some real valued measurable function f and an is larger than Ef (X) . We present an approximating scheme for this density together with an explicit rule for the determination of the value of k which produces a given accuracy bound. Numerical simulation argue in favor of this proposal and show that k can be chosen quite close to n for large values of n. This result is optimal in the sense that it coincides with the exact conditional d density in the gaussian case. Examples when X is R valued will also be presented. This result is a step in the direction of fast Importance Sampling procedures for rare event simulation.(so called zero variance estimators); the asymptotic variance of the resulting estimate shows that the sampling density based on the approximation

101 of the conditional density provides a clear gain over the classical tilting scheme. Simulation results support the asymptotic expansions leading to the evaluation of the variance.

Asymptotic analysis of traffic lights performance under heavy-traffic assumption. Speaker: Ekaterina Bulinskaya, Moscow State University, Russia. Co-authors: Larisa Afanasyeva, Elena Yarovaya. The main drawback of Markov models for traffic-lights performance introduced in our previous research is exponential distribution of intervals between lights switchings. To analyze the impact of this assumption we consider a model with constant intervals. An algorithm is proposed to calculate imbedded Markov chain stationary probabilities and mean length of a queue at crossroads. Although the difference between two models is slight for traffic intensity ρ ∼ 0.5, it is significant for ρ close to 1. We investigate the queue length behavior as ρ → 1. Weak convergence of normalized characteristics (waiting time, queue length etc.) under the heavy traffic assumption to exponential ones is established. To prove this we use the asymptotic equivalence of these characteristics to supremum of an integervalued random walk with zero reflecting boundary. We only assume that all the random values determining the model are mutually independent and possess the third moment. The system’s structure is inessential (e.g. we can consider multi-lane highways). It is important to obtain the normalizing coefficients taking into account the system structure and distributions of underlying random variables. For complex models it leads to interesting problems of point processes theory. The research was partially supported by RFBR grant 10-01-00266.

From micro to macro description of a system of stochastic particles subject to nonlocal interactions. Speaker: Vincenzo Capasso, Universitàdegli Studi di Milano, Italy. Co-authors: Daniela Morale. The development of a general and coherent framework for modeling collective behavior of biological populations, built from the basic stochastic processes acting at the individual level, is far from complete since the complexity of biological organization raises nontrivial mathematical problems. Here we report on a rigorous mathematical derivation of a macroscopic model of aggregation, scaling up from a microscopic description of a family of individuals subject to aggregation/repulsion, described by a system of Itôtype stochastic differential equations. We refer to a model proposed and analyzed by the authors in a series of papers. The basic model describes the interaction of a system of a finite number of particles subject on one hand to a “force” of aggregation depending upon a “long-ranged” nonlocal gradient of the spatial distribution of the total population; on the other hand individuals are supposed to be subject to a “force” of repulsion depending upon a “short-ranged” local gradient of the population. Both components are assumed to depend upon the empirical spatial distribution of the total population. The stochasticity is modeled by a family of independent standard Brownian motions, so that the Lagrangian description of the movement of a population of N individuals is given via a system of N Itôtype stochastic differential equations. For the Eulerian description we refer to the time evolution of the spatial distribution of the total population, i.e. the empirical measure associated with the system of N particles. For a finite and small number N of individuals the empirical measure suffers significant stochastic fluctuations. But a “law of large numbers” shows how for N tending to infinity the stochastic fluctuations tend to disappear. We show in a

102 rigorous way that the dynamics of a limit measure whose density is a solution of a deterministic integro-differential equation describing the evolution of the mean-field spatial density of the population. In particular the derivation is performed in the case of diffusion coefficients, depending upon N; possibly vanishing for N tending to infinity. In this last case the limiting PDE would be degenerate thus causing problems for the uniqueness of the solution; the authors provide conditions for the existence and uniqueness of an entropy solution. If the diffusion coefficient is not allowed to vanish, the consequent regularization guarantees the existence and uniqueness of the solution of the limiting PDE, a fact that helps in the rigorous derivation of such limit.

The distribution of the domination number of a family of random catch digraphs based on one-dimensional data. Speaker: Elvan Ceyhan, Ko¸cUniversity, Turkey. I present a new kind of proximity graphs called proportional-edge proximity catch digraphs (PCDs) in a randomized setting. PCDs are a special kind of random catch digraphs that have been developed recently and have applications in statistical pattern classiﬁcation and spatial point pattern analysis. PCDs are also a special type of intersection digraphs; and for one-dimensional data, the proportional-edge PCD family is also a family of random interval catch digraphs. We present the exact (and asymptotic) distribution of the domination number of this PCD family for uniform (and non-uniform) data in one dimension. We also provide several extensions of this random catch digraph by relaxing the expansion and centrality parameters, thereby determine the parameters for which the asymptotic distribution is non-degenerate. We observe sudden jumps (from degeneracy to non- degeneracy or from a non-degenerate distribution to another) in the asymptotic distribution of the domination number at certain parameter values.

Kernel estimators of density functionals with reduced bias. Speaker: Jos´eE. Chac´on, Universidad de Extremadura, Spain. Co-authors: Carlos Tenreiro. We pose the problem of estimating the integral of squared density derivatives making use of kernel methods. This is a well-known problem but some of its features remain unexplored. All the existing approaches deal with the problem of bandwidth selection from an asymptotic point of view. Here we study the properties of a new bandwidth choice that annihilates the exact bias, rather than its asymptotic counterpart. We show that the selection of this bandwidth on the basis of model-based clustering techniques leads to a reduction in bias as compared to previous kernel approaches.

Generalized scale invariance in finite range systems. Speaker: Sandra Chapman, University of Warwick, UK. Co-authors: K. Kiyani, N. W. Watkins, B. Hnat, R. M. Nicol. Statistical scaling is one of the key characteristics of many degree of freedom systems that are driven, dissipating and out of equilibrium. Physical realizations of such systems are usually of finite range and are observed in a time stationary state over restricted time intervals. A ubiquitous, but not well understood, aspect of finite range turbulence is generalized scale invariance or extended self similarity (ESS) which is seen in both hydrodynamic

103 and magnetohydrodynamic (MHD) turbulent flows, for example, in the solar wind. The nature of this correction to scale invariant inertial range turbulence captures features of the structure and dynamics of the turbulent flow and when seen from the perspective of finite sized scaling makes contact with critical phenomena. We will use observations of astrophysical MHD turbulence to find the single generalized scaling function that captures statistical scaling of the largest (outer) scales that is at the heart of the observed ESS, and is insensitive to conditions of the flow. This points to a universal property of finite range MHD turbulence. We will also discuss the limitations of observations that are finite length sequences in determining scaling exponents. Estimating the scaling exponents relies upon estimating the moments, or more typically structure functions, of the probability density of the differenced time series. If the probability density is heavy tailed, extreme values that are poorly represented statistically strongly influence the scaling behavior of the moments. We give a method for extracting the scaling exponents and quantifying their uncertainty for self- affine processes. We develop and demonstrate the method for a synthetically generated symmetric α stable Lévyprocess, and show an astrophysical application.

Option Pricing and estimation under stochastic volatility with long-memory. Speaker: Alexandra Chronopoulou, Institut national de recherche en informatique et automatique (IN- RIA) Nancy-Grand Est, France. Co-authors: Frederi Viens. We treat the problem of option pricing under a stochastic volatility model that exhibits long-range dependence. We model the price process as a Geometric Brownian Motion with volatility evolving as a fractional Ornstein- Uhlenbeck process. We assume that the model has long-memory, thus the memory parameter H in the volatility is greater than 0.5. Although the price process evolves in continuous time, we are only able to collect observations in discrete time. Using historical stock price information we adapt an interacting particle stochastic ﬁltering algorithm to estimate the stochastic volatility empirical distribution. In order to deal with the pricing problem we construct a multinomial recombining tree using sampled values of the volatility from the stochastic volatility empirical measure. Moreover, we describe how to estimate the parameters of our model, including the long-memory parameter of the fractional Brownian motion that drives the volatility process using an implied method. Finally, we compute option prices on the S&P 500 index and we compare our estimated prices with the market option prices.

An urn-based spatio-temporal shock model for cancer growth modeling. Speaker: Pasquale Cirillo, University of Bern, Switzerland. Co-authors: JürgHüsler. We propose a new spatio-temporal shock model, in which several systems interact on a lattice. As in standard shock models, every system is subject to random shocks of random magnitude that can make it fail, but these shocks are no more independent, as they depend on the behavior of the neighboring systems. For example, we assume that the probability of a given system to fail increases with the number of failed neighbors, following the principle of cascading failures. In more detail, we propose an urn model for such interacting systems. Every system is represented by an urn that is sampled. Every urn contains balls of different colors and each color represents a state of the system (for example no default - default). After every sampling, the urns are Polya- reinforced, according to their reinforcement rule. Differently from other works in the literature, reinforcement is

104 now a function of three different components: 1) time (the so-called temporal contagion), 2) the configuration of the lattice and, in particular, of the clique to which every system belongs (spatial contagion), and finally 3) a random element (the impact of fate). After showing the construction of the model and its statistical and probabilistic properties, we also provide an application related to cancer growth modeling. In fact, if we assume that the lattice represents a cellular tissue and the urns are the cells, our model can be used to study the spread of cancer through the entire tissue, starting from a first sick cell.

Convergence of quasi-stationary distributions of sequences of birth-death processes. Speaker: Damian Clancy, University of Liverpool, UK. Consider a sequence of birth-death processes, each on ﬁnite state-space, with absorption at the upper boundary and with all other states forming a single communicating class. Each such process possesses a unique quasi- stationary distribution on the non-absorbing states. In the limit as the upper boundary tends to inﬁnity, we derive conditions under which the sequence of quasi-stationary distributions converges to the stationary distribution of a limiting birth-death process on the non-negative integers. This extends a result obtained previously by Keilson and Ramaswamy in that we allow for dependence between the birth and death rate parameters and the size of the state space. The general result may be applied to yield new rigorous limit results for the quasi-stationary distribution of the susceptible-infective-susceptible (SIS) infection model and of a Pearl-Verhulst type population model proposed by N˚asell.

Multipower variation for Brownian semistationary processes. Speaker: JoséManuel Corcuera, Universitat de Barcelona, Spain. Co-authors: O.E. Barndorff-Nielsen, M. Podolskij. In this paper we study the asymptotic behavior of power and multipower variations of processes Y : Z t Yt = g(t − s)σsW (ds) + Zt, −∞ where g : (0, ∞) → R is deterministic, σ > 0 is a random process, W is the stochastic Wiener measure, and Z is a stochastic process in the nature of a drift term. Processes of this type serve, in particular, to analyze data of velocity increments of a fluid in a turbulence regime with spot intermittency σ. The purpose of the present paper is to determine the probabilistic limit behavior of the (multi)power variations of Y , as a basis for studying properties of the intermittency process σ. Notably the processes Y are in general not of the semimartingale kind and the established theory of multipower variation for semimartingales does not suffice for deriving the limit properties. As a key tool for the results a general central limit theorem for triangular Gaussian schemes is formulated and proved. Examples and an application to realized variance ratio are given.

On the distribution of a damped telegraph random process. Speaker: Antonio Di Crescenzo, Universit`adi Salerno, Italy. Co-authors: Barbara Martinucci.

The telegraph process has been studied in the past by many authors aiming to describe a random motion at

105 constant speed on the real line, whose velocity alternates according to a Poisson process. Various one-dimensional generalizations of the telegraph process have been proposed in the literature towards cases with more than two velocities, cases with velocity changes governed by non-homogeneous Poisson process or by alternating renewal process, etc. In this contribution we study a stochastic process that describes a finite velocity damped motion on the real line. Differently from the telegraph process, the random times between consecutive velocity changes have exponential distribution with linearly increasing parameters. We obtain the probability law of the process, which admits a logistic stationary limit in a special case. Various results on the distributions of the maximum of the process and of the first-passage time through a constant boundary are also presented.

A central limit theorem and its applications to multicolor randomly reinforced urns. Speaker: Irene Crimaldi, Universit`adi Bologna, Italy. Co-authors: Patrizia Berti, Luca Pratelli, Pietro Rigo.

As regards asymptotics in urn models, there is not a unique reference framework. Rather, there are many (inge- nious) disjoint ideas, one for each class of problems. Well known examples are martingale methods, exchange- ability, branching processes, stochastic approximation, dynamical systems and so on. Those limit theorems which unify various urn problems, thus, look of some interest. We focus on the CLT. While thought for urn problems, our CLT is stated for an arbitrary sequence of real random variables. Accordingly, it potentially applies to every urn situation, but it has generally a broader scope: it deals with the general problem of the rate of convergence of predictive distributions and empirical distributions for dependent data. To illustrate how the CLT works, we show two applications: multicolor randomly reinforced generalized Polya urns and generalized Poisson-Dirichlet sequences. The ﬁrst one regards the case of an urn model for which the leading eigenvalue of the mean reinforce matrix is not simple. The second one regards the case of a “Poisson-Dirichlet type” sequence with values in a discrete space. This talk is based on some papers in collaboration with Patrizia Berti, Luca Pratelli and Pietro Rigo.

Application of overrepresentation for estimating results of tracking surveys. Speaker: Wieslawa Dabala, Public Opinion Research Center, Poland.

Samples for surveys are sampled from the same population, with the same stratiﬁcation and sampling scheme.The sample sizes after sampling are identical or almost identical. Strata are overrepresented. For estimating sizes of samples in strata, both fractions of sizes of strata in population and response rates in previous researches were used. Sampling from strata is a two-stage process. Probabilities of selecting units of population are not equal. The samples are partially realized and response rates are diﬀerent in strata. The realized sample sizes are smaller than the selected sample sizes. The base estimated parameter of the population is the total value. The other parameters are its combinations. Statistics adjusted by weights are used as estimators of the population parameters. The calculation of weights included probabilities of selecting units, response rates in strata and external statistical data for correcting proportions. The estimation of variance of estimators gives complex formulas, and

106 in practice it can be done with simpliﬁed methods, with the use of resampling.

A numerical method for expected penalty-reward function in a Markov-modulated jump- diﬀusion process. Speaker: Peter Diko, Universidad Carlos III de Madrid, Spain. Co-authors: Miguel Us´abel.

We propose a generalisation of a Cramér-Lundberg risk model perturbed by a diffusion. Aggregate claims of an insurer follow a compound Poisson process and premiums are collected at constant rate with additional random fluctuation. The insurer is allowed to invest the remaining surplus into a risky asset with volatility dependent on the level of the surplus which permits the incorporation of rational investment strategies as those proposed by Berk and Green (2004). The return on investment is modulated by a Markov process which generalizes previously studied settings allowing the evolution of the interest rate in time. Gerber-Shiu expected penalty-reward function is studied in this context, including ruin probabilities (a first-passage problem) as a special case. We obtain a second order integro-differential system of equations that characterizes the function of interest. As no closed-form solution exists, we use a numerical procedure based on Chebyshev polynomial approximation through a collocation method to obtain the solution of the studied system. Finally, we illustrate the procedure presenting some examples and discussing the results.

Changepoint model for high yield processes. Speaker: Mavroudis Eleftheriou, Aristotle University Of Thessaloniki, Greece. Co-authors: Farmakis Nikolas.

The modern production methods have minimized the non-conforming items almost in every production procedure giving rise to the development of new techniques for high yield processes. The traditional techniques of statistical process control (SPC), including the usual control charts, fail to satisfactorily detect the items where the process is set out of control. Additionally, the majority of the current control charts are designed to function efficiently only under specific assumptions related to the distributional behavior of the examined quality features. Thus, the demand of developing new non-parametric control charts, effectively applicable on high yield processes, is becoming bounden. In this paper we evolve the nonparametric changepoint model developed by Zhou (2009), and we appropriately modify it to be applicable to attribute high yield processes. Simulations are conducted to determine the non-parametric control limits of the new control chart and the optimal values of its parameters. Additional comparison simulations reveal the superiority of the new proposed control chart.

A sex talk: The matchmaking paradox. Speaker: Iddo Eliazar, Holon Institute of Technology, Israel. Co-authors: Igor Sokolov.

Medical surveys regarding the number of heterosexual partners per person yield diﬀerent female and male averages

107 - a result which, from a physical standpoint, is impossible. In this talk we establish a statistical model explaining this “matchmaking paradox”. We consider a bipartite graph with N male and N female nodes (N >> 1), and B bonds connecting them (B >> 1). Each node is associated a random “attractiveness level”, and the bonds connect to the nodes randomly - with probabilities which are proportionate to the nodes’ attractiveness levels. The population’s average bonds-per-nodes B/N is estimated via a sample average calculated from a survey of size n (n >> 1). A comprehensive statistical analysis of this model is carried out, asserting that: (i) the sample average well estimates the population average if and only if the attractiveness levels possess a ﬁnite mean; (ii) if the attractiveness levels are governed by a “fat-tailed” probability law then the sample average displays wild ﬂuctuations and strong skew - thus providing a statistical explanation to the matchmaking paradox.

Dynamical comparisons and ageing properties of system maintenance policies review and recent results. Speaker: Laureano Escudero, Universidad Rey Juan Carlos, Spain. Co-authors: Eva Mar´ıaOrtega.

Different maintenance policies have been defined in Reliability theory to improve the performance of systems operating under environments. To reduce the frequency of the failures and to minimize the inactivity time due to sudden failures are two objectives for these policies (see Wang (2002)), that include among them, reparation policies and preventive replacement for items that have failed, and replication by active and passive redundancy of components of the systems. The lifetime of engineering Systems subjected to wear or damage has been described also by the shock models. From a probabilistic point of view, this lifetime is a random sum (see Bai et al. (2006)). In this context, several criteria have been defined and applied for the dynamical comparison of maintenance policies for systems by different statistics, for example by the number of failures at each time point, or the inter-arrival times for the failures for any observed failure (see Kamae, Krengel and O’Brien (1977), Block, Langberg and Savits (1990), Block and Savits (1994), Yue and Cao (2001) y Belzunce, Ortega and Ruiz (2005,2006b)); as well as multivariate comparisons in the sense of Shaked and Szekli (1995). Another related problem consists of studying the ageing properties of Systems that describe different patterns of evolution of systems subjected to wear due to environmental or/and intrinsic operating conditions (see Barlow and Proschan (1963), Lai and Xie (2006)). Non parametric statistical inference methods have been developed in order to fit failure time or duration data to these classes of distributions, and also to decide about the stochastic comparison from two random samples. In this work, we provide a review about dynamical comparisons and ageing properties of maintenance policies in the literature. Then we present some results on comparison and ageing for different failure reparation models, as the discrete-time pure birth shock model, general shock models, and the relevation counting process, and other related reparation policies; as well as other maintenance policies, as the warm standy redundancy. The construction of stochastic bounds provides a criterion to evaluate how these policies improve the lifetime of the System. Some other consequences on the comparison results and the ageing properties are discussed as well.

108 Covering the whole space with Poisson random balls. Speaker: Anne Estrade, Universite Paris Descartes, France. Co-authors: Hermine Bierme, Jean-Baptiste Gouere.

We consider Poisson random balls in Rd, with the pair (center, radius) being given by a Poisson point process in RdxR+. We investigate necessary and suﬃcient conditions, based on the intensity measure of the Poisson process, for covering the whole space with the union of the balls. We exhibit a disjunction phenomenon between the covering with large balls (low frequency) and the covering with small balls (high frequency). Concerning the second type covering, we prove the existence of a critical regime and give an explicit value of the critical intensity. We also compare with other critical regimes appearing in continuum percolation.

Optimality of trunk reservation for an M/M/k/N queue with several types of customers and holding cost. Speaker: Eugene Feinberg, Stony Brook University, USA. Co-authors: Fenghsu Yang.

We study optimal admission to an M/M/k/N queue with several customer types. The cost structure consists of revenues collected from admitted customers and holding costs, both of which depend on customer types. The goal is to ﬁnd an admission policy that minimizes average rewards per unit time. Under natural assumptions we show that an optimal policy has a trunk reservation form. Previously problems with the same holding costs for all customers have been studied in the literature.

Queueing analysis of error-prone production systems. Speaker: Dieter Fiems, Ghent University, Belgium. Co-authors: Ahmad Al-Hanbali, Herwig Bruneel.

Production systems are conceived to always operate and never break down. In reality, production systems do sometimes break down, causing a loss of production capacity and additional backlog of pending production orders. If such breakdowns occur frequently, their impact on the overall operation of the production system cannot be neglected. We here consider an abstract production system which is inherently error prone. The system is capable of producing different types of products with different random production time requirements. Errors may be detected during or after production and invoke random repair times. Moreover, the arrivals are temporarily blocked while the system is under repair. Such an assumption comes naturally in a multi-stage production system where buffer space between the consecutive production stages is limited. To assess the performance of the production system at hand, a discrete-time queueing system is constructed and analyzed by means of a probability generating function approach. We obtain expressions for various performance measures such as the moments of the production delay and the queue size. We then illustrate our approach by means of some numerical examples.

109 Some classiﬁcation results of generalized mixtures of Weibull distributions. Speaker: Manuel Franco, Universidad de Murcia, Spain. Co-authors: Juana-Mar´ıaVivo.

Weibull distributions and their mixtures have been widely used in many applications, since they exhibit a broad range of shapes for density and failure rate functions. The generalized mixture of Weibull distributions provide more flexibility for modeling data sets allowing negative mixing weights. Besides, generalized mixture of Weibull distributions with common shape parameter arise under formation of some structures of systems, such as series and parallel systems, i.e. the minimum and maximum order statistics, which are the most usual structures in the real life. In particular, the extreme statistics from some bivariate Weibull models with dependent components and same shape parameter have predominantly Weibull or generalized mixtures of Weibull components with the same shape parameter. Recently, Franco and Vivo (2009, Constraints for generalized mixtures of Weibull distributions with a common shape parameter, Statistics and Probability Letters, 79, 1724-1730) discussed necessary and sufficient conditions to be a valid probability model and characterized the generalized mixtures of three or fewer Weibull. In this work, we study the classification of the generalized mixtures of two or three Weibull distributions with a common shape parameter, in the IFR and DFR classes. Furthermore, we apply the classification results of the generalized mixtures to classify the ageing of the extreme order statistics, maximum and minimum, from some bivariate Weibull models.

Inference for the diﬀerence of two percentile residual life functions. Speaker: Alba Mar´ıaFranco Pereira, Universidad Carlos III de Madrid. Co-authors: Rosa E. Lillo, Juan Romo.

In Joe and Proschan (1984) the percentile residual life orders were introduced, but they were extensively studied in Franco-Pereira et al. (2009). In this paper, some interpretations and properties of these stochastic orders were given and some applications in reliability theory and finance were described. Given the advantages of the percentile residual life orders, specially in practical situations, it is convenient to develop a statistical tool to test whether two independent random samples have underlying random variables which are close with respect to a percentile residual life order. In this work, we present a nonparametric method for constructing confidence bands for the difference of two percentile residual life functions. This functional data analysis technique incorporates bootstrap resampling and the concept of statistical depth. The confidence bands provide us with evidence of whether two random variables are close with respect to some percentile residual life order. The practical performances of the bands are evaluated through simulation. Some applications with real data are also given.

Statistical characterization of the time-delay for web-based networked telerobots. Speaker: Ana Gago-Ben´ıtez, Universidad de M´alaga,Spain. Co-authors: Juan-Antonio Fern´andez-Madrigal, Cipriano Galindo, Ana Cruz-Mart´ın.

Networked telerobots are a class of robots remotely controlled over general purpose networks, like the Internet, that have important applications such as robotic telecare, telesurgery, space operation, etc. They are composed of

110 heterogeneous components: network, operating systems, application software, interfaces... most of them having a stochastic response-time behavior. In spite of this, their human teleoperators still need a timely flow of sensory information from the robot. To maintain this flow close to the optimal, we need a good on-line statistical estimation of its delay, which improves with accurate mathematical models. Classical robotic teleoperation employs deterministic components in most parts of the system, so the sensory flow is not an issue. Recently, an important amount of research has been done on stochastic networked control systems (NCS), but still considering the other components deterministic. The networking community has also explored stochastic communications, but again focusing only on the network response. Finally, approaches to control the timing of data flow in multimedia applications also exist, but they do not need to cope with the strict time requirements for controlling robots. This paper presents a thorough statistical characterization of the sensory flow in a web-based networked telerobot system, which exhibits abrupt changes in the delay, such as regimes, bursts and outliers. Our study considers all the stochastic components of the system and a diversity of scenarios. We analyze the statistical models that best fit the actual time delays and therefore are suited for optimizing the on-line estimation required for remote control.

Optimal paths for autonomous vehicle based on Markovian readings. Speaker: Nancy Garcia, Universidade Estadual de Campinas, Brazil . Co-authors: Ronaldo Dias, Adriano Zambom.

This paper describes an efficient algorithm to find a smooth trajectory joining two points A and B with minimum length constrained to avoid fixed subsets. The basic assumption is that the locations of the obstacles are measured several times through a mechanism that corrects the sensors at each reading using the previous observation. The proposed algorithm is based on the penalized nonparametric method introduced by Dias, Garcia and Zambom (2008) that uses confidence ellipses as a fattening of the avoidance set. In this paper we obtain consistent estimates of the best trajectory using Monte Carlo construction of the confidence ellipse.

On a discrete time risk model with interest. Speaker: Maude Gathy, Universit´eLibre de Bruxelles, Belgium. Co-authors: Claude Lef`evre.

A classical discrete time risk model assumes that an insurance company owns an initial amount u ≥ 0 and receives, at the beginning of the time periods, a fixed premium c > 0. At the end of the n-th time period, this company has also to pay the amount Xn , the total amount of the claims that occurred during this period, n ∈ N. The Xn’s constitute a sequence of i.i.d positive random variables. The ruin of the company happens when the surplus of the company becomes strictly negative. A Cramér-Lundberg bound on the ultimate ruin probability is available as well as a closed expression for the finite time ruin probability (see e.g. Bowers et al. (1986) and Lefèvreand Loisel (2009)). The present work is concerned with an extended discrete time risk model proposed by Lefèvreand Picard (2006) where the successive premiums cn are deterministic and nonuniform, and the successive claim amounts Xn are independent and nonidentically distributed. In addition, the economic

111 environment is taken into account by incorporating a sequence of fixed rates of interest in per periods. For this generalized model, we first provide a Cramér-Lundberg bound for the ruin probability over any finite time horizon. This bound depends on the length of the time horizon through an appropriate adjustment coefficient. Then, we consider the possibility for the insurer to use proportional reinsurance. The existence and the determination of a retention level maximizing the adjustment coefficient is investigated. Finally, the results obtained are illustrated with some applications.

Controlled stochastic networks in heavy traﬃc: Convergence of value functions. Speaker: Arka Gosh, Iowa State University, USA.

Here we study a scheduling control problem for a broad family of networks under heavy traffic with general interarrival and service times, probabilistic routing and an infinite horizon discounted linear holding cost. Diffusion control problems, that have been proposed as approximate models for the study of these critically loaded controlled stochastic networks, can be regarded as formal scaling limits of such stochastic systems. However, to date, a rigorous limit theory that justifies the use of such approximations for a general family of controlled networks has been lacking. In this work we show that, under broad conditions, the minimum achievable asymptotic cost (value function) of the network control problem is equal to that of the associated diffusion control problem. This scaling limit result, in addition to giving a precise mathematical basis for the above approximation approach, suggests a general strategy for constructing near optimal controls for the physical stochastic networks by solving the associated diffusion control problem.

Random ﬂights with Dirichlet-distributed interarrival times. Speaker: Alessandro De Gregorio, Universit`adegli Studi di Roma “La Sapienza”, Italy. Co-authors: Enzo Orsingher.

The infinite speed-models (like the Brownian motion) are not suitable to represent the real processes. We deal with a class of stochastic models with finite velocity, called random flights, describing a random motion as follows. A particle initially located at the origin of a frame of reference of the multidimensional real space chooses the direction of its motion with a spherically uniform distribution. It continues to move in that direction with constant velocity until the particle collides with an obstacle. Then, with the same spherically uniform law, it chooses again the direction of its second step and this is maintained until a new collision. This process goes on until time t. The sample paths described by the moving particle appear as straight lines with sharp turns and look like polygonals made up of randomly oriented segments of random length. Many papers considered the length of the time steps exponentially distributed. We focus our attention on the case in which the joint distribution of the interarrival times follows a Dirichlet law. We are able to derive the exact distribution of the position of the particle at time t conditionally on the number of the steps. Applications of random flights concern the motions of gas particles in collisions or microorganisms moving on laboratory slides.

112 Estimation of the spectral probability measure. Speaker: Armelle Guillou, Universit´ede Strasbourg, France. Co-authors: Philippe Naveau, Alexandre You.

First, we will introduce a new approach, developed by You et al. (2010), for statistical estimation problems in extreme value theory. This method relies on the use of a folding transformation, defined by Corcoran and Schneider (2003) in the context of ”perfect sampling” which allows to connect the center of the distribution and its tail. This transformation has been studied in the univariate independent and identically distributed case and an adaptation of the classical Peaks-Over-Thresholds approach has been proposed. Simulations tend to indicate that this method improves significantly the performances of extreme quantiles estimators in finite sample situations. In this talk, our aim is to extend the concept of the folding transformation in a multivariate extreme value framework with some application to statistical estimation problems. We will start by introducing a multidimensional version of the folding transformation and the statistical procedure which allows us to build the folded version of the sample. Then, we will propose a class of estimators of the spectral probability measure based on the folded sample and we will show their weak consistency. Finally, we will illustrate the performances of these estimators through numerical applications and simulations.

Predicting residential losses in Florida by the public model. Speaker: Sneh Gulati, Florida International University, USA. Co-authors: Shahid Hamid, Golam Kibria, Steve Cocke, Jean-Paul Pinelli.

As an environmental phenomenon, hurricanes cause significant property damage and loss of life in coastal areas almost every year. Although a number of commercial loss projection models have been developed to predict the property losses, only a handful of studies are available in the public domain to predict damage for hurricane prone areas. The State of Florida has developed an open, public model for the purpose of probabilistic assessment of risk to insured residential property associated with wind damage from hurricanes. The model comprises of three components; viz. the atmospheric science component, the engineering component and the actuarial science component. The atmospheric component includes modeling the track and intensity life cycle of each simulated hurricane within the Florida threat area. Based on historical hurricane statistics, thousands of storms are simulated allowing determination of the wind risk for all residential Zip Code locations in Florida. The wind risk information is then provided to the engineering and actuarial components to model damage and average annual loss, respectively. The actuarial team finds the county wise loss and the total loss for the entire state of Florida. The computer team then compiles all information from atmospheric science, engineering and actuarial components, processes all hurricane related data and completes the project. The model was submitted to the Florida Commission on Hurricane Loss Projection Methodology for approval and went through a rigorous review and was revised per the suggestions of the commission . The final model was approved for use by the insurance companies in Florida by the commission. At every stage of the process, statistical procedures were used to model various parameters and validate the model. This paper presents a brief summary of the main components of the model (meteorology, vulnerability and actuarial) and then focuses on the statistical validation of the same.

113 Estimation of mean survival time and reliability function in case of exponential distribution. Speaker: Rahul Gupta, University of Jammu, India.

Exponential distribution plays an important part in life-testing problems and is the most widely exploited model in this area. Early work by Sukhatme (1937) and later work by Epstein and Sobel (1953,1954,1955) and Epstein (1954,1960) gave numerous results and popularized the exponential as a lifetime distribution, especially in the area of industrial life testing. Sequential techniques have been utilized by several researchers to deal with various inferential problems related to one-parameter and two-parameter exponential distributions. For some citations one may refer to Basu (1971), Starr and Woodroofe (1972), Mukhopadhay (1974), Mukhopadhay and Hilton (1986), Chaturvedi and Shukla (1990) and Chaturvedi (1996). The purpose of the present work is two-fold. First, we consider sequential estimation of the mean survival time and reliability function corresponding to the two-parameter exponential distribution. We address the problem of interval estimation of the mean survival time using sequential technique. Sequential procedures are adopted, based on the maximum Likelihood estimator and uniformly minimum variance unbiased estimator of the scale parameter. A comparative study of the two sequential procedures is done and they are proved to be “asymptotically efficient and consistent”. Secondly, we consider the problem of construction of “fixed-ratio-width” confidence interval for the reliability function, for addressing which a sequential procedure is proposed. The sequential procedure is proved to be “asymptotically efficient and consistent”. For all these sequential procedures, simple techniques of obtaining the asymptotic distribution of the stopping time are derived.

Large deviation inequalities for N-demimartingales and negatively associated random variables. Speaker: Milto Hadjikyriakou, University of Cyprus, Republic of Cyprus. Co-authors: Tasos C. Christoﬁdes.

In recent years, dependence concepts including positive and negative association introduced by Esary et al. (1967) and Joag-Dev and Proschan (1983) respectively, have been the focus of substantial research activity. Among the various results presented are extensions and generalizations. In particular, Newman and Wright (1982) introduced the concept of a demimartingale and a demisubmartingale as a generalization of the notion of martingales and submartingales. The deﬁnition is a rather technical one and serves, among other things, the purpose of studying in a more general way the behavior of the partial sum of mean zero associated random variables. The class of N-demimartingales generalizes in a natural way the concept of negative association and includes as special cases martingales with respect to the natural choice of σ-algebras. For this class of random variables, a number of maximal and other inequalities were obtained by Christoﬁdes (2003) and Prakasa Rao (2004, 2007). In this paper we prove Azuma’s inequality for N-demimartingales and as a corollary we obtain an exponential inequality for negatively associated random variables and related asymptotic results. We also provide a Marcinkiewicz-Zygmund inequality for nonnegative N-demimartingales which is the key inequality for obtaining inequalities for tail probabilities.

114 Spectral gap for a colored disordered lattice gas of generalized exclusion processes. Speaker: Zeghdoudi Halim, Badji-Mokhtar University, Algeria. Co-authors: Ali Bey Touati, Haccne Boutabia.

We consider a system of colored disordered lattice gas in a volume V of Zd. Using a result of Zeghdoudi and Boutabia (2009), where they propose a new computation for the canonical measures for a colored disordered lattice gas and spectral gap of exclusion processes. The aim of the present paper is to calculate the spectral gap for a colored disordered lattice gas of generalized exclusion processes which plays an important role in the study of hydrodynamic limit.

Populations, catastrophes and extinction probability: Algorithmic methods. Speaker: Sophie Hautphenne, Universit´eLibre de Bruxelles, Belgium. Co-authors: Guy Latouche.

A large number of systems in biology and telecommunications may be modeled by continuous-time multitype branching processes. In order to determine the extinction probability of such processes, one has to find the minimal nonnegative solution of a polynomial matrix fixed point equation. As soon as individuals do not behave independently of each other, this fixed point equation does not hold anymore. This may happen for instance when an external process, such as a catastrophe process, influences the evolution of the whole population. In that case, the extinction probability may alternately be obtained from the distribution of the population size as time increases to infinity. We focus on a special class of multitype branching processes called Markovian binary trees, and we assume that they undergo catastrophe events controlled by a Poisson process or more generally by a Markovian arrival process. We show that the population size distribution is solution of a functional integral equation, and we present different algorithmic methods to compute the extinction probability.

A Monte Carlo method for problems of optimal stochastic control with convex value functions. Speaker: Juri Hinz, National University of Singapore, Singapore.

We present a method for the calculation of the optimal policy for inﬁnite horizon optimal control problems whose value function is convex. Control problems of this type appear in many applications and encompass important examples arising in the area of partially observed Markov decision processes. We show that the calculation performance can be improved by a modiﬁcation of the classical least- square approach. Our adaptation is based on the convexity property of conditional expectation, valid in our framework.

On the multi-armed bandit problem and its Lagrangian relaxation. Speaker: Peter Jacko, Basque Center for Applied Mathematics, Spain.

We present a novel proof of optimality of an index policy for the classic multi-armed bandit problem and several related problems including the tax problem and the job sequencing problem. A uniﬁed model containing all these problems as special cases is developed. We then optimally solve its Lagrangian relaxation and construct an

115 optimal solution in the form of an index policy for the non-relaxed model. Our approach yields complementary insights to existing proofs and a novel formula for characterizing the value function.

Likelihood-based inference for correlated diﬀusions. Speaker: Konstantinos Kalogeropoulos, London School of Economics, UK. Co-authors: Petros Dellaportas, Gareth O. Roberts.

We address the problem of likelihood based inference for correlated diffusion processes using Markov chain Monte Carlo (MCMC) techniques. Such a task present two interesting problems. First, the construction of the MCMC scheme should ensure that the correlation coefficients are updated subject to the positive definite constraints of the diffusion matrix. Second, a diffusion may only be observed at a finite set of points and the marginal likelihood for the parameters based on these observations is generally not available. We overcome the first issue by using the Cholesky factorization on the diffusion matrix. To deal with the likelihood unavailability, we generalize the data augmentation framework of Roberts and Stramer (2001 Biometrika 88(3):603-621) to d-dimensional correlated diffusions including multivariate stochastic volatility models. Our methodology is illustrated through simulation based experiments and with daily EUR /USD, GBP/USD rates together with their implied volatilities.

Some convergence results in a modiﬁed leader election algorithm. Speaker: Ravi Kalpathy, George Washington University, USA. Co-authors: Hosam Mahmoud.

We consider a serialized coin-tossing leader election algorithm that proceeds in rounds in which it is decided that the players are eliminated (when they throw heads) or move to the next round (when they throw tails) according to the outcome of biased coin flips. The process is perpetuated until a winner is chosen. Unlike the conventional leader election algorithm, if at any stage, all players throw heads, we stop the process. We investigate two parameters in our modified leader election problem: the depth Dn for a particular player or in other words the number of rounds a randomly chosen contestant survives and the speed Xn of the algorithm in terms of the total number of coin flips. Using analytic techniques such as the Mellin Transform and poissonization, we develop the mean, variance and moment generating function for Dn and asymptotically it turns out to be a geometric random variable. The moment calculations for Xn using the analytic techniques increases in complexity with each higher moment. We circumvent this problem by using the contraction method and we demonstrate that the distribution of Xn (suitably normalized) approaches a normal limiting random variable that is the fixed-point solution of a distributional equation in the Wasserstein metric space.

An asymptotic expansion for the tail of compound sums of Burr distributed random variables. Speaker: Dominik Kortschak, Universit´ede Lausanne, Switzerland. Co-authors: Hansj¨orgAlbrecher.

In this talk we show that it is possible to write the Laplace transform of the Burr distribution as the sum of four

116 series. This representation is then used to provide a complete asymptotic expansion of the tail of the compound sum of Burr distributed random variables. Furthermore it is shown that if the number of summands is ﬁxed, this asymptotic expansion is actually a series expansion if evaluated at suﬃciently large arguments.

Error distribution of the ensemble Kalman ﬁlter update. Speaker: Andrey Kovalenko, CIPR-University of Bergen, Norway. Co-authors: Trond Mannseth, Geir Nævdal.

Bayesian data assimilation methods have been widely used in recent years. Kalman filter is a recursive method of updating the system state given a time series of noisy measurements provided that the prior distribution is Gaussian and the system is linear. Given a pdf of the prior state and the data likelihood, a Bayesian update is performed. The mean and covariance evolution in the Kalman filter is governed by a system of linear equations. In case of large systems, however, it is infeasible to store large matrices, and matrix multiplication becomes a problem. A Monte-Carlo approximation of the Kalman filter (ensemble Kalman filter, or EnKF) has been introduced to avoid these problems. A computationally reasonable number of samples from the prior distribution is generated, and each of them is updated according to the Kalman equations, where the covariance matrix is replaced by its estimate from the ensemble. Sampling errors lead to artificial effects, such as spurious correlations, deteriorating the estimates of the system state. There is lack of methods quantifying the error of the EnKF update. Using random matrix theory, we derive the conditional distribution of the norm of the deviation of the EnKF estimate from the Kalman filter estimate, given the sample mean from the prior. The distribution depends explicitly on the ensemble size, model dimension and locations of the observed components of the state vector. We also derive a distribution of the sample covariance after the data assimilation step.

Multivariate order based on extremality notion. Speaker: Henry Laniado Rodas, Universidad Carlos III de Madrid, Spain. Co-authors: Rosa E. Lillo, Juan Romo.

We propose a family of multivariate stochastic orders using the extremality of a point respect to a distribution function in a ﬁxed direction. The extremality is characterized by the probability measure of an oriented convex cone. This new ordering generalizes the well-known upper orthant and lower orthant order. Properties and some applications will be shown.

Limit theorems for stationary Markov additive processes. Speaker: James Ledoux, INSA de Rennes, France. Co-authors: D´eborah Ferre, Loic Herve.

Let (Xt,Yt)t≥0 be a discrete or continuous time Markov additive process such that the driving general state space Markov chain (Xt)t≥0 is stationary, with π as invariant distribution. We assume that (Xt)t≥0 satisﬁes a L2(π)-spectral gap property. Some ρ-mixing arguments and the spectral method are used to derive a central

117 limit theorem and speciﬁc reﬁnements (local limit theorem, Berry-Esseen bound, Edgeworth development) for the additive component (Yt)t≥0. Our moment conditions are close or equal to those of the i.i.d. case. Such results apply to various instances of MAPs of interest in applied probability. This includes discrete time or continuous time additive functionals of (Xt)t≥0 which are basic processes in performability analysis or in some statistical issues such as limit theorems for M-estimators.

Markov couplings, stochastic orders, and stochastic relations. Speaker: Lasse Leskel¨a, Aalto University, Finlandia.

Stochastic orders are powerful tools for approximating random processes whose distributions cannot be computed explicitly. For example, two stationary Markov processes can be ordered without explicit knowledge of the limiting distributions by means of an order-preserving Markov coupling. In this talk I will present a sharp characterization for the existence of order-preserving Markov couplings, which is based on a new notion of stochastic relations. This existence result is complemented with a recursive algorithm for computing the maximal subrelation of a given order which is stochastically preserved by two of Markov processes. The theory is illustrated with applications related to multidimensional random walks, stochastic networks, and interacting particle systems. The talk is based on the article: Stochastic relations of random variables and processes. Journal of Theoretical Probability, to appear. arXiv:0806.3562.

On the Laplace transform of some functionals related to the variation of Brownian motion with drift. Speaker: Rafal Lochowski, Warsaw School of Economics, Poland.

In the paper Truncated variation of Brownian motion with drift (Bull. Pol. Acad. Sci. Math. 56(2008), no. 4, 267-281) we defined truncated variation of Brownian motion with drift. Truncated variation differs from regular variation by neglecting jumps smaller than some fixed constant. We prove that truncated variation is a random variable with finite exponential moments of any order. We also define two closely related quantities - upward truncated variation and downward truncated variation. The defined quantities may have some interpretation in financial mathematics. Exponential moment of upward truncated variation may be interpreted as the maximal possible return from trading a financial asset in the presence of flat commission when the dynamics of the prices of the asset follows a geometric Brownian motion process. We calculate the Laplace transform with respect to time parameter of the “regular” Laplace transform of the upward and downward truncated variations. As an application of the obtained formula we give an exact formula for expected value of upward and downward truncated variation. We also give exact (up to universal constants) estimates of the expected values of the mentioned quantities. Phase-like transition may be observed, when the drift parameter, time parameter or truncation constant are changed. It is also possible to derive formulas for higher moments of (upward, downward) truncated variation from the presented formula.

118 The stochastic goodwill problem: A monotone follower model with discretionary stopping. Speaker: Polly Lon, London School of Economics, UK. Co-authors: Mihail Zervos.

We formulate and solve a problem that combines the features of the so-called monotone follower of singular stochastic control theory with optimal stopping. In particular, we consider a stochastic system whose uncon- trolled state dynamics are modeled by a general one-dimensional Itôdiffusion. The aim of the problem that we solve is to maximize the utility derived from the system’s state at the discretionary time when the system’s control is terminated. This objective is reflected by the performance criterion that we maximize, which also penalizes control expenditure as well as waiting. The model that we study is motivated by the so-called goodwill problem, a variant of which is concerned with how to optimally raise a new product’s image, e.g., through advertising, and with determining the best time to launch the product in the market.

A new theory of inter-temporal equilibrium for security markets. Speaker: Jaime Alberto Londo˜noLondo˜no, Universidad Nacional de Colombia, Colombia.

A new theory of inter-temporal equilibrium for security markets in a continuous time setting with Brownian Filtrations for complete and incomplete markets is developed. A simple characterization of equilibrium when agents maximize a state dependent utility functional, as proposed in J.A. Londoño(2009), is given. The model presented requires agents with the same type of utilities that belongs to any of the classical utilities structures, but otherwise heterogeneous with possible different incomes streams, different credit restrictions, different and arbitrary initial allocations of wealth, and with possible negative wealth’s. It is shown that any equilibrium market is consistent with non-arbitrage. Some simple examples that include economies when securities pay no dividends or when there are no income for agents are presented. The theoretical framework used is a generalization of markets when the processes are Brownian Flows on Manifolds.

Central limit theorem for the number of near-records. Speaker: F. Javier L´opez, Universidad de Zaragoza, Spain. Co-authors: Raul Gouet, Gerardo Sanz.

Near-records in a sequence of random variables Xn, n ≥ 1, are observations within a ﬁxed distance of the current maximum. More precisely, given a > 0, Xn is a near-record if Xn ∈ (Mn−1 − a, Mn−1], where Pn Mn = max{X1,...,Xn}. We establish the asymptotic normality of Dn = i=1 1l{Xi ∈ (Mi−1 − a, Mi−1]}, the number of near-records among the ﬁrst n observations, when the underlying random variables are independent and identically distributed, with common continuous distribution.

Convergence of option rewards for multivariate price processes. Speaker: Robin Lundgren, M¨alardalen University, Sweden. Co-authors: Dmitrii Silvestrov.

119 American type options with general payoﬀ functions possessing polynomial rate of growth are considered for multivariate Markov price processes. Convergence results are obtained for optimal reward functionals of American type options for perturbed multivariate Markov processes.

Volatility in the Black-Scholes formula for ﬁnitely many strikes. Speaker: Olivia Mah, Monash University, Australia. Co-authors: Kais Hamza, Fima Klebaner.

We investigate the compatibility between the Black-Scholes option pricing formula and non-constant volatility stock price models. The assumption of constant volatility of the Black-Scholes stock price model, from which the Black-Scholes formula is derived, has long drawn criticisms from researchers and practitioners in the industry. Studies have shown that volatility does vary with strike prices and time-to-maturities. Despite this drawback, the formula is still widely used in the industry for pricing options. So we ask: are there stock price models which are compatible with the formula but in which volatility is non-constant? Here, we consider models for which volatility is a function (possibly random) of time t. A previous study has shown that if the Black-Scholes formula is to hold for “all strike prices”, then the volatility parameter must be a constant. That is, the formula is not compatible with non-constant volatility models.

Maxima of moving maxima of continuous functions. Speaker: Thomas Meinguet, Universite catholique de Louvain, Belgium.

Maxima of moving maxima of continuous functions (CM3) are max-stable processes aimed at modeling extremes of continuous phenomena over time. They are defined as Smith and Weissman’s M4 processes with continuous functions rather than vectors. After standardization of the margins of the observed process into unit-Fréchet, CM3 processes can model the remaining spatio-temporal dependence structure. CM3 processes have the property of joint regular variation. The spectral processes from this class admit particularly simple expressions. Further- more, depending on the speed with which the parameter functions tend toward zero, CM3 processes fulfill the finite-cluster condition and the strong mixing condition. For instance, these three properties put together have implications for the expression of the extremal index. A method for fitting a CM3 to data is investigated. The first step is to estimate the length of the temporal dependence. Then, by selecting a suitable number of blocks of extremes of that length, clustering algorithms are used to estimate the total number of different profiles. The number of parameter functions to retrieve is equal to the product of these two numbers. They are estimated thanks to the output of the partitioning algorithms in the previous step. The full procedure only requires one parameter which is the range of variation allowed among the different profiles. The dissimilarity between the original CM3 and the estimated version is evaluated by means of the Hausdorff distance between the graphs of the parameter functions.

120 Stochastic comparisons for time transformed exponential models. Speaker: Julio Mulero, Universidad de Alicante, Spain. Co-authors: Franco Pellerey, Rosario Rodr´ıguez-Gri˜nolo.

Different sufficient conditions for stochastic comparisons between random vectors have been described in the literature. In particular, conditions for the comparison of random vectors having the same copula, i.e., the same dependence structure, may be found in Müllerand Scarsini (2001). We provide here conditions for the comparison, in the usual stochastic order sense and in weaker stochastic orders, of two time transformed exponential bivariate lifetimes having different copulas. Some examples of applications are provided too.

Asymptotic behavior of a system of stochastic particles subject to nonlocal interactions. Speaker: Daniela Morale, Universit`adegli Studi di Milano, Italy. Co-authors: Vincenzo Capasso.

We discuss a model describing the interaction of a system of a finite number of particles subject on one hand to a “force” of aggregation depending upon a “long-ranged” nonlocal gradient of the spatial distribution of the total population. On the other hand individuals are supposed to be subject to a “force” of repulsion depending upon a “short-ranged” local gradient of the population. Both components are assumed to depend upon the empirical spatial distribution of the total population. The stochasticity is modelled by a family of independent standard Brownian motions, so that the Lagrangian description of the movement of a population of N individuals is given via a system of N Itôtype stochastic differential equations. In particular we study the long time behavior of the system for a fixed number N of stochastic differential equations. In the model discussed here, an additional term has been included in the drift term, describing possible intrinsic dynamics of each individual particle. The particular choice of this term is for the time asymptotic behaviour of the system. We first discuss the behavior of the purely interacting and diffusive system, and show that in this case the system cannot admit a nontrivial invariant distribution. On the other hand, under suitable conditions on a “localizing” potential U it does admit a nontrivial invariant distribution to which the system converges; we notice that the requirements on U about its convexity are less restrictive with respect to previous literature.

Computing weighted-mean trimmed regions in any dimension. Speaker: Karl Mosler, Universit¨atzu K¨oln,Germany. Co-authors: Pavel Bazovkin.

Trimmed regions are a powerful tool of multivariate data analysis. They describe a probability distribution in Euclidean d-space regarding location, dispersion and shape, and they order given multivariate data with respect to their centrality. Dyckerhoﬀ and Mosler (2009) have introduced the class of the so-called weighted-mean trimmed regions, which have a substantial interpretation in terms of multivariate set-valued risk measures that are coherent. We construct an exact algorithm to compute all weighted-mean trimmed regions of a given data cloud in arbitrary dimension. These trimmed regions are convex polytopes in Rd. To calculate them, the algorithm builds on methods from computational geometry. A characterization of a region’s facets is used, and information about

121 the adjacency of the facets is extracted from the data. A key problem consists in ordering the facets. It is solved by the introduction of a tree-based order. The algorithm will be implemented as an R-package. Based on the exact algorithm, approximate calculations can be developed and their precision evaluated.

Populations, catastrophes and extinction probability: Analytical bounds for the extinction criteria. Speaker: Giang Nguyen, Universit´eLibre de Bruxelles, Belgium. Co-authors: Guy Latouche, Sophie Hautphenne.

Branching processes are powerful tools for modelling, among other things, the evolution of populations. We consider the situation where there are catastrophes arriving according to a Poisson process that might eﬀect various sub-groups of a population in diﬀerent ways. Athreya and Karlin (1971) show that a population will become extinct almost surely if and only if a particular limit is non-positive. This limit is the largest Lyapunov exponent of a Markovian product of matrices, where each matrix is the expected increase in population between two catastrophes. An analytic structure for this limit is not yet known; hence, the value of this limit is usually obtained by simulations. In this presentation, we show that using duality techniques, we can derive analytic upper and lower bounds for this limit.

Mixture modeling and convex ordering for bio-inspired communication, rooted network and maintenance. Speaker: Eva Mar´ıaOrtega, Universidad Miguel H´ernandez,Spain. Co-authors: Laureano Escudero, Concepci´onParedes.

The probabilistic analysis of different performance measures associated with stochastic models in engineering and biotechnology has become a major research issue due to the complexity of these systems. Recently, Escudero, Ortega and Alonso (2009) provided some results in this direction. This communication provides a Bayesian approach for the stochastic modeling and the analysis of the effect of statistical dependencies on the variability of some applied models. Some bio-inspired communication models, rooted networks, system maintenance policies, and other related problems are addressed. Bio-inspired communication models and rooted networks have been used to model evolution in heterogeneous computing and communication systems, that are characterized by heterogeneous nodes, restricted communication channels and strongly dynamic environments, among others. Our framework captures the uncertainties of the model by random environmental parameters. The distribution of the performance measure is defined by a mixture having arbitrary mixing distribution for the environmental parameters, which retain the dependence in the model. Our analysis is based on convex type orderings to compare the variability of the systems operating under two different environments and stochastic directional convexity properties of the families of parameterized random variables that define these models. Stochastic bounds for these measures are obtained when the environments fulfil some dependence properties. Bounds for higher moments of the random variables yield more useful probabilistic bounds than the expected value and many interesting risk measures are increasing convex transformations of the random variables, and they can be bounded by using

122 the convex order. Especially, bounds are computable from some dependence notions deﬁned in terms of the independent version of the random vector of parameters. We address some related optimization problems that are solved from comonotone environmental parameters. This Bayesian framework can be applied for data analysis and simulation from non-parametric dependence tests in the literature.

Understanding the eﬀect of infectiveness on dose-response and epidemic model by stochastic orderings. Speaker: Isabel Ortega, Centro de Salud El Pl`aElche, Spain. Co-authors: Eva Maria Ortega, Laureano Escudero.

The variability of the infected population (or the susceptible population) at a given time for some susceptible- infected-removed (SIR) epidemic models has been applied as a measure on the spread of the epidemics (see e.g., Isham (2005)). With a more general scope, dose-response models describe the probability of a specific response from exposure to a specific pathogen, in a population, and have been applied in toxicology, food-pathogen infections and other diseases (see e.g., Haas (2002) ). Heterogeneity of populations from the infectives or the susceptibles has been considered to take into account the effect of several environmental, exposure and clinical factors, that may affect the infectious capacity; as well as some individual features that affect on the disease incidence. Stochastic orderings have become useful tools for comparing the variability of some epidemic models, under different environments, especially from the work of the mathematician Claude Lefèvre(see Denuit, Lefèvre and Utev (1999), Escudero, Ortega and Alonso (2010), Ortega and Escudero (2010), among others). Experi- mental studies have assessed on correlations arising between some parameters related to the infectiveness, during propagation. In this work, we explore some stochastic models for the population growth motivated by some problems of interest in medicine and biology, that we emphasize. In general, the number of infectives under several epidemic models and dose-response models follows a binomial distribution, based on an infection probability. We present a general simple framework to model the probability distribution of infective (susceptible) populations, as a mixture with random parameters determined by the infectiveness or the dose. We study the effect of uncertain parameters on the mixtures by using stochastic orderings. These results allow the risk assessment based on the variability of the population and other biometric measures. A discussion on related frameworks in the literature is provided.

Functional data analysis of wave profiles. Speaker: Joaqu´ınOrtega, Centro de Investigaciónen MatemáticasA.C. (CIMAT), México. Co-authors: Cristina Gorrostieta, George H. Smith.

In this work we use Functional Data Analysis techniques for the analysis of wave profiles recorded during a North- Sea storm lasting several days. The analysis focuses on the relationship between the significant wave height for 20-minute periods and the shape of the mean wave for the corresponding periods. We also look at the relation between the first and second derivatives of the mean wave and study the phase diagram as a function of the significant wave height. We compare the results with a simulated Gaussian storm. Additionally, we study the

123 modes of variation for waves during diﬀerent storm periods and for waves under normal conditions using functional principal components, and compare the results.

Semi-Markov reward moments for a closed model in healthcare systems. Speaker: Aleka Papadopoulou, Aristotle University of Thessaloniki, Greece. Co-authors: Sally McClean, George Tsaklidis.

In this paper we extend our previous semi-Markov reward model which attached costs to duration in states by including costs of making a transition from one state to another. In the healthcare domain such transition costs allow us to evaluate the overall costs of therapy or clinical intervention where an operation or other treatment may be an option. This model can be used for strategic approaches to planning and evaluating long term patient care. Results are obtained for the moments of interval costs for every member of the system and of the total cost at any time and in the steady state. The results show the potential of the model to demonstrate diﬀerential costs of diﬀerent therapeutic strategies and explore optimal solutions.

Towards a uniﬁed theory of queueing systems. Speaker: M. F. Ramalhoto, Universidade T´ecnicade Lisboa, Portugal.

The aim of this paper is two folds: 1. To present an overview of the Little’s laws and their extensions. 2. To provide an exploratory discussion concerning new trends and emerging directions towards a uniﬁed theory of queueing systems mainly based on those relationships.

Non-identiﬁability of the two-state markovian arrival process. Speaker: Pepa Ram´ırez-Cobo, Universidad de Sevilla (IMUS), Spain. Co-authors: Rosa E. Lillo Rodr´ıguez,Michael P. Wiper.

In this paper we consider the problem of identifiability of the two-state Markovian Arrival process (MAP2). In particular, we show that the MAP2 is not identifiable and conditions are given under which two different sets of parameters, induce identical stationary laws for the observable process.

Hemachandra numbers, indian music, and patterns in coin tossing. Speaker: M. B. Rao, University of Cincinnati, USA. Co-authors: Subramanyam Kasala.

Fibonacci Numbers arise in a variety of contexts. Hemachandra numbers are the same as Fibonacci numbers but they predate Fibonacci by at least one hundred years. Indian musicians have been using Hemachandra numbers in their compositions. The presentation will begin with an outline of these historical perspectives. We then go on elucidate how these numbers arise again in certain coin tossing problems. The exploration leads to generalized Fibonacci numbers. We obtain generating function of these generalized Fibonacci numbers. We use probabilistic

124 recurrence relation methodology to achieve our objectives.

Penultimate models for the reliability of series-parallel and parallel-series systems. Speaker: Paula Reis, CEAUL and EST-Politecnic Institut of Set´ubal,Portugal. Co-authors: Lu´ısaCanto e Castro.

When we study the exact reliability function of some technological systems, we frequently find complex structures, due to the large number of systems components and the way the operating process uses such components. Real examples of this kind of systems arise in transport networks of oil, gas and water; also on telecommunication and electrical energy distribution networks and on charge and discharge networks. Usualy in these cases it is better to admit that the number of system components goes to infinity so as to find asymptotic models that give a good interpretation of the reliability. Using the characterization of domais of attraction for maxima and minima, for the known generalized extreme value distributions, Reis and Canto e Castro (2009) identified limit models for the reliability function, conveniently normalized, in the case of a regular and homogeneous series-parallel system. However, in certain systems, the reliability function, can be better approximated by a different reliability function than by its own limit. Such an approximation is called penultimate or pre-asymptotic and yields an improvement of the convergence rate. The study of the penultimate behaviour for the i.i.d. case, has been developed by different authors, such as, Cohen (1982), Gomes e Pestana (1987) and Kaufmann (2000). In this talk we will use results in Gomes and de Haan (1999), where distribution functions whose right tails verify von Mise’s first and second order conditions and also a penultimate condition are considered, to obtain penultimate and ultimate approximations for the reliability function, conveniently normalized, of regular and homogeneous series-parallel and parallel-series systems.

An insurance risk model with Parisian implementation delays. Speaker: Jean-Fran¸coisRenaud, University of Waterloo, Canada. Co-authors: David Landriault, Xiaowen Zhou.

Inspired by Parisian options, a new deﬁnition of ruin is proposed: the surplus process can spend a certain amount of time under a pre-speciﬁed default level before recovering, otherwise default is said to have occured. The same idea is applied to a dividend barrier strategy. Using the modern language of scale functions, we study dividend payments and Gerber-Shiu functions in such an insurance risk model driven by a spectrally negative Levy process.

New characterisations of multivariate lifetime distribution. Speaker: Rosario Rodr´ıguez-Griñolo, Universidad Pablo de Olavide, Spain. Co-authors: Fernández-Ponce, JoséMar´ıa,Pellerey, Franco.

Some well-know univariate aging classes of lifetimes distributions, such that IFR, DMRL and NBUE, have been characterized by means of properties of their quantile functions. In this work, we consider the multivariate versions of these characterizations, deﬁning new multivariate aging classes based on properties of the multivariate

125 u-quantiles. For it, we consider the multivariate u-quantiles introduced in O’Brien (1975) and a minor modification of the notion of upper-corrected orthant introduced in Fernández-Ponce and Suárez-Lloréns(2003). Using these notions, we provide definitions of multivariate failure rate and of multivariate expected residual lifetime. Then, we give the definitions of different classes of multivariate lifetimes distributions, generalizing in a natural way the univariate aging classes mentioned above. Relationships between such multivariate aging classes are also investigated.

The sinh-arcsinhed t distributions. Speaker: Juan Francisco Rosco, Universidad de Extremadura, Spain. Co-authors: M.C. Jones, Arthur Pewsey.

In recent years, various “skew-t” distributions have been proposed within the statistical literature. Important such cases are the distributions of Azzalini & Capitanio (2003), Jones & Faddy (2003) and Ma & Genton (2004?). In this paper we employ the sinh-archsinh transformation of Jones & Pewsey (2009) as a means of deﬁning what we refer to as the ‘sinh-arcsinhed t’ distribution. Instead of centering the sinh-arcsinh distribution on one particular t distribution and then using an extra parameter to control tailweight, we use the degrees of freedom of Student’s t distribution to control the tailweight in the usual way. After including location and scale parameters, we obtain a four-parameter family of distributions containing symmetric as well as asymmetric members with varying tail weights. We will present the fundamental properties of the new family and illustrate likelihood based inference for its parameters using a data set of glass ﬁbre strength measurements.

On the first passage time for bivariate diffusion processes. Speaker: Laura Sacerdote, Universitàdegli Studi di Torino, Italy. Co-authors: Elisa Benedetto, Cristina Zucca.

The First Passage Time (FPT) distribution of one dimensional diffusion processes through boundaries has been the object of numerous studies. This fact has allowed to determine some closed form solution for the problem while reliable and efficient algorithms exist for numerical evaluations. Despite its importance in various application the analogous results for the two dimensional case are scarce. Motivated by a two compartment neuronal model describing the Interspike Intervals we consider here a FPT problem for a bivariate Ornstein Uhlenbeck process. In particular we focus on the FPT of the first component through a constant boundary. We develop a numerical schema that allows to evaluate the FPT probability density function. We compare this distribution with the analogous for the one dimensional case. Possible generalizations to other processes of the proposed method are also discussed.

Stabilization and limit theory for random polytopes. Speaker: Tomasz Schreiber, Nicolaus Copernicus University, Poland. Co-authors: Pierre Calka, Joseph E. Yukich.

126 We present new results for functionals of random convex polytopes in unit balls in Euclidean spaces, obtained using general theory of geometric stabilization for point processes. The functionals considered include volumes, mean widths and more generally intrinsic volumes of all orders, as well as numbers of faces of arbitrary dimensions. The generating process is assumed Poisson with intensity regularly varying at the boundary. For these objects, we develop a local scaling theory in terms of paraboloid growth and hull processes, extending recent work by Schreiber and Yukich and characterizing functional and measure-level limits for the local boundary processes of random polytopes and their curvature measures. Then, using theory of stabilization, we obtain global functional and measure-level Gaussian limits and variance asymptotics for the functionals of interest. We conclude the talk mentioning similar applications of these techniques to large zero-cells of isotropic hyperplane tessellations.

Shock and wear models under matrix-analytic methods. Speaker: Maria del Carmen Segovia, Universidad de Granada, Spain. Co-authors: Rafael P´erez-Oc´on.

We consider the shock model of Esary et al (1973) under the matrix-analytic methods. A first paper using this methodology to this classical model is the one of Neuts and Bhattacharjee (1981), introducing a phase-type renewal process as model of arrival of shocks. A new extension of the model, assuming that the arrival of shocks follow a Markovian arrival process (MAP), is studied by the authors (2009). In the present work, it is assumed that the system undergoes damage after every shock. The quantity of damage is random, and then, several types of models can be considered: the cumulated shock model, the maximum shock model, and the run shock model. The quantity of damage produced by the shocks is finite, and it can be deterministic or random. For these models, the reliability is calculated and it is given in an algorithmic form. A comparison of the different models completes the study.

A stochastic SIR epidemic model on a network of individuals with household structure. Speaker: David Sirl, University of Nottingham, UK. Co-authors: Frank Ball, Pieter Trapman.

Many models for the spread of infectious disease make signiﬁcant simplifying assumptions concerning the homogeneity of individuals in the population of interest and/or the homogeneity of their mixing. We propose a model for the spread of an SIR (susceptible → infective → removed) epidemic which draws together two ways of incorporating heterogeneity of individuals in such a model—partitioning the population into households and using a random graph to model a social network—whilst maintaining a high degree of mathematical tractability. We discuss the analysis of the model from both theoretical and practical viewpoints and describe several extensions to the model with emphasis on the inclusion of multiple types of individual.

Sequential data-adaptive bandwidth selection for dependent discrete-time processes. Speaker: Ansgar Steland, RWTH Aachen University, Germany.

127 The problem to detect structural changes in a sequence of observations appears in many areas of applications such as communication engineering, econometrics and finance as well as environmetrics. It is well known that the general problem to detect an arbitrary change in the distribution of the series can be solved by methods for the basic problem to detect a change in mean. Thus we study a class of detection rules based on kernel-weighted statistics which addresses this issue. It is well known that quantities such as the asymptotic average normed delay now depend on the kernel and the bandwidth parameter. The same applies to the weak limit of the associated sequential empirical process, both for stationary as well as for non-stationary series of observations. Suppose we have fixed a kernel. Basing our procedure on a slightly modified prediction statistic, we investigate the probabilistic properties of a sequential approach where a cross-validation criterion is minimized at N time points, where N may tend to infinity at some rate. We establish a consistency result of the procedure which holds true for a large class of weakly dependent processes. Indeed, under slightly modified conditions compared to the i.i.d. case, we are able to show consistency for near epoch dependent (NED) series. This notion covers many linear and nonlinear time series models used in areas such as engineering or finance and allows to handle a couple of well known examples of which are of some interest but not strong mixing.

The power log-GARCH model. Speaker: Genaro Sucarrat, Universidad Carlos III de Madrid, Spain. Co-authors: Alvaro´ Escribano.

Exponential models of autoregressive conditional heteroscedasticity (ARCH; after Engle (1982)) are attractive in empirical analysis because they guarantee non-negativity of the conditional variance in estimation, and because they enable richer autoregressive dynamics. However, currently there exists no proof that enables consistent estimation of general classes of exponential ARCH models. Here, we provide such a proof. Specifically, we prove a result that enables consistent estimation of univariate and multivariate power log-GARCH models under very general assumptions when the power is fixed, via vector ARMA representations. Also, the power log-GARCH model can be viewed as nesting certain classes of stochastic volatility models, including the common ASV(1) specification. The result enables ordinary inference strategies regarding the coefficients in univariate and multivariate power log-ARCH specifications, and our simulations suggest the methods compares well with Gaussian QML (in the standardised error).

Optimal policies under full history dependence: Robbins’ problem. Speaker: Yvik Swan, Universit´eLibre de Bruxeles, Belgium. Co-authors: F. T. Bruss.

A decision maker samples (sequentially) a given distribution n times. After each observation, he must decide either to keep its value or to reject it. All decisions are supposed to be final. Upon completion of the sampling process, the cost of the decision maker’s policy is defined as the final rank of the chosen observation. The objective is to devise stopping rules which minimize the expected cost. At first view Robbins’ problem is a simple secretary problem, whose solution is given by the standard tools of optimal stopping. It is also closely related

128 to the problem of minimizing the expected value, known as Moser’s problem, whose solution is well known. In truth, Robbins’ Problem is, however, much more challenging: the optimal rule is an intractable function of the full history of the process. The problem is therefore intrinsically inﬁnite dimensional, and any hope for progress lies in ﬁnding an alternative approach that bypasses this complexity. In this talk we will describe a number of such alternatives. We will also address the issue of the history dependence, with a particular emphasis on the link between Moser’s and Robbins’ problems which, as will be seen, brings the problem into a new light.

Limit laws for maxima of a stationary random sequence with random sample size. Speaker: Maria da Gra¸caTemido, Universidade de Coimbra, Portugal. Co-authors: J. Husler, A. Freitas.

Let {Xn} be a stationary sequence of real random variables, {kn} be a nondecreasing sequence such that kn+1/kn tends to a constant not less than 1 and let {Tn} be a real sequence such that Tn/kn converges in probability to a positive random variable D. Consider that the limit distribution G of Mkn with an appropriate linear normalization exists, being in this case a max-semistable distribution. In this work we assume that {Xn} veriﬁes an adaptation of the usual dependence restriction of Leadbetter, appropriate for the max-semistable context, and an additional mixing condition which is needed to deal with random sample sizes. Under these conditions, we prove that the maxima MTn , sampled at random times Tn and under the same linear normalization, converges in distribution to a mixture of G and the distribution of D. Examples of a Gaussian stationary model and of an integer-valued moving average model are given.

On the γ-order generalized Gaussian. Speaker: Paula Camelia Trandaﬁr, University de Valladolid, Spain. Co-authors: Christos P. Kitsos, Thomas Toulias.

The multivariate normal distribution N(µ, Σ) plays an important role in the Fischer’s entropy type information measures, J(X), Cover and Thomas (2006). Thus the measure has been extending introducing and extra parameter γ and the generalized Fisher’s entropy type measure, Jγ(X), has been extensively discussed by Kitsos and Tavoularis (2009), while for γ = 2 coincides with the existing one, ie. J2(X) = J(X). The introduced hyper multivariate normal distribution, KT γ(µ, Σ), Kitsos and Tavoularis (2008), generalize the multivariate normal and supports the new entropy type information measures. Notice that KT 2(µ, Σ) = N(µ, Σ). In this paper the general form of the γ-order multivariate normal distribution KT γ(µ, Σ) is given, its parameters are studied, and the behaving of KT γ(µ, Σ) is discussed, in comparison with the multivariate normal.

Light-traﬃc analysis of queueing systems with train arrivals. Speaker: Koen De Turck, Ghent University, Belgium. Co-authors: Dieter Fiems, Sabine Wittevrongel, Herwig Bruneel.

Input traﬃc at various nodes in packet switched telecommunication networks typically exhibits correlation at

129 various time scales. If queueing theory is to be used for assessing the performance of these buffers, arrival correlation must be modeled accurately. Train-arrival models have been successfully applied to this end. Arrivals are organised in larger entities called trains, correlation being introduced by the duration of these trains, the arrival process of the trains and the arrivals within the trains. Although the literature on train-arrival models is consid- erable, a key constraint remains: the load of a single train must equal or exceed the server capacity. Lifting this constraint is the aim of this contribution. We investigate performance of a discrete-time single-server queueing system with train arrivals, where each train generates packets according to a Bernoulli process. To the best of our knowledge, the queueing problem at hand cannot be solved by exact analytical techniques. Therefore, we focus on light-traffic approximations. In particular, we develop a Taylor series expansion in the parameter of the above-mentioned Bernoulli processes. Then, by means of a Padéapproximation, we improve on our light-traffic results by taking into account either the heavy-traffic limit or the solution for train-arrival models in which trains always produce packets. Finally, we verify our approximation by some numerical results.

A spatio-temporal Poisson model to estimate the density of blue whales in the Antartide. Speaker: Mar´ıaCruz Valsero Blanco, Universidad de Valladolid, Spain. Co-authors: Prieto Gonz´alez,Rocio, Adam, Olivier.

Population models are standard tools to evaluate the size of a biological population. Very often, these models are based on counts from a single site or population. Nevertheless, populations ussually move and spread out across multiple sites. So we need models that take into account the mobility of populations in a specific area, consequently, the new models will provide reliable methods to determine size, density and distribution of population stocks. Our data come from the records of sounds produced by blue whales. These data must be processed to produce a multiple count time-series. But not every whale in the area will produce a sound and a single whale can produce more than one sound. To include these facts in the model, we introduce a Poisson process with two parameters, one spatial that deals with the density of whales in an area and other temporal parameter that measures the intensity of sounds detected by a unitary whale in an interval of time. We suppose that every whale acts independent of each other. With these hypotheses, we develop the distribution spatio-temporal of the process and we use the distribution to calculate the likelihood function, to find a maximum that would produce goods estimators of the parameters spatial and temporal. To find the maximum of the likelihood function it is not an easy question; in order to calculate it, we have an initial estimator calculated using the moments method.

On the pdfs’ of the state sizes of a continuous time homogeneous Markov system with ﬁnite state capacities. Speaker: George Vasiliadis, Aristotle University of Thessaloniki, Greece. Co-authors: G. Tsaklidis.

In the present paper the evolution of a continuous time homogeneous Markov system with finite state capacities is studied. The members that overflow due to the finite state capacities are supposed to leave the system and enter an absorbing state. In order to investigate the variability of the state sizes, the time dependent intensity

130 matrix for the transitions is evaluated, and a formula concerning the derivative of the moments of the state sizes is derived. Then the distributions of the state sizes as well as the distribution of the absorption time are given. The theoretical results are illustrated by a numerical example.

A semi-parametric approach for time-to-event forecasting. Speaker: Alejandro Veen, IBM TJ Watson Research Center, USA.

Many companies face event forecasting problems with time-to-event duration distributions that are typically skewed to the right. Examples include forecasting of invoice payments or loan defaults. While traditional survival analysis focuses on modeling (relative) event occurrence risks in order to quantify the eﬀects of certain covariates, businesses often need a forecast for the actual occurrence times, or at least a useful interval-based forecast such as event occurrence probabilities for the upcoming months, quarters, or years. While there might be suﬃcient data to estimate the main part of the time-to-event duration distribution empirically, there is often too little data to estimate the right tail of the distribution in such a non-parametric way. This work presents a non-parametric approach that combines the empirical distribution estimate for the main part of the distribution with with a parametric distribution estimate for the right tail while identifying an appropriate breakpoint adaptively. An example will illustrate the methodology and the performance of this time-to-event forecasting approach.

Benchmarking restless bandit index policies in a multitarget tracking model. Speaker: Soﬁa Soledad Villar, Universidad Carlos III de Madrid, Spain. Co-authors: Jose Ni˜no-Mora.

We consider a Markov control model for the optimal dynamic scheduling of M steerable beams to track N moving targets in a multi-sensor system. We formulate such a multitarget tracking model as a discrete-time multiarmed restless bandit problem (MARBP) with real-state projects. The resulting formulation allows us to contemplate two optimality criteria: discounted and average performance objectives, accounting for tracking-error variance and measurement costs. The optimal control policy for such an MARBP, characterized by the dynamic programming equations, is generally intractable. This fact motivates research on the design of heuristics, such as priority-index policies, which are both of low complexity and near optimal. We address such issues by deploying Whittle’s (1988) index policy for the MARBP formulation, and we resolve the challenging issues of indexability (existence of the index) and index evaluation by applying a method recently introduced by Ni˜no-Mora for the analysis of real-state restless bandits. Such an indexation methodology allows us to address the additional challenge of carrying out large-scale experiments for benchmarking the performance of restless bandit index policies under realistic scenarios. The computational results obtained demonstrate the tractability of index evaluation, the substantial performance gains that the restless bandit index policy achieves against myopic policies advocated in previous work, and their relatively small suboptimality gaps.

Asymptotic properties of non-parametric estimators of a semi-Markov model used for earth-

131 quake prediction. Speaker: Irene Votsi, Aristotle University of Thessaloniki, Greece. Co-authors: G. Tsaklidis, N. Limnios, E. Papadimitriou.

The present study is a probabilistic seismic hazard assessment for certain areas of Greece. A semi-Markov model is applied where the classiﬁcation of states is based upon seismotectonic criteria. Non-parametric estimators of the semi-Markov kernel, Markov renewal function, transition function and hazard rate are calculated for selected data sets taken from an earthquake catalog that covers the instrumental period. The asymptotic properties of these estimators as the time interval becomes large are studied through this application. Evaluation of conﬁdence intervals concerning these estimators contributes to the earthquake prediction in the study areas.

Fairness and eﬃciency in waiting times for polling models with the k-gated service discipline. Speaker: Sandra (A.C.C.) van Wijk, Technische Universiteit Eindhoven, The Nehterlands.

We consider a polling system, where a single server cyclically serves the queues, with positive switch-over times. Our goal is to minimize the differences in the mean waiting times at each of the queues, i.e. to achieve maximal fairness, without giving up too much on the efficiency of the system. For this, we introduce the k-Gated service discipline, which can be seen as a hybrid version of the well known exhaustive discipline (very efficient, less fair) and gated discipline (less efficient, usually more fair). Upon arrival of the server at queue i, it services the queue consecutively an integer number of times, ki, according to the gated discipline. That is, a first gate closes and only the customers before this gate are served, then a second gate closes, and again only the customers before this gate are served, etcetera, until this is done ki times, or until the queue becomes empty. We derive the distribution of the waiting times, a pseudo conservation law for the weighted sum of the mean waiting times, and the fluid limits of the waiting times. The latter we use for optimization of the ki’s, and we provide heuristics for well working settings.

A Cluster identiﬁcation framework illustrated by a ﬁltering model for earthquake occurrences. Speaker: Zhengxiao Wu, National University of Singapore, Singapore.

A general dynamical cluster identification framework including both modeling and computation is developed. The earthquake declustering problem is studied to demonstrate how this framework applies. A stochastic model is proposed for earthquake occurrences that considers the sequence of occurrences as composed of two parts: earthquake clusters and single earthquakes. We suggest that earthquake clusters contain a “mother quake” and her “offspring”. Applying the filtering techniques, we use the solution of filtering equations as criteria for declustering. A procedure for calculating MLE’s and the most likely cluster sequence is also presented.

Asymptotic theory of change diagnosis in the distribution of a Markov-modulated random se-

132 quence. Speaker: Kazutoshi Yamazaki, Osaka University, Japan. Co-authors: Savas Dayanik.

We develop an asymptotic theory of the change diagnosis problem modeled by Dayanik & Goulding (2009). Based on a sequence of observations, one needs to detect an unobservable change at the earliest and identify its change type accurately. The observation process is modeled in terms of some functional of an underlying hidden Markov chain. We propose computationally tractable sequential decision strategies and show their asymptotic optimality under two Bayesian formulations. We verify the results numerically using an example where the observation process is normally distributed.

Branching walks in inhomogeneous environments and their applications in the theory of epidemics. Speaker: Elena Yarovaya, Moscow State University, Russia. Co-authors: Larisa Afanasyeva, Ekaterina Bulinskaya.

The theory of epidemics has demonstrated the importance of developing stochastic models in which the evolution- ary processes depend on the structure of a medium. The examples of such models are branching random walks. Models of continuous-time branching random walks on the multidimensional lattice are considered. The underlying random walk is assumed to be symmetric. The main results are obtained for the branching medium containing a single source of branching situated at the origin. In this sense the medium is spatially inhomogeneous. The oﬀspring reproduction law is deﬁned by the intensities of Markov birth-and-death processes at the origin. One of the main problems in models of branching random walks is investigation of the asymptotic behavior of particles number of at an arbitrary point of the lattice as well as the whole particles population. The long-term behavior both for the local and total particle populations is studied. General methods are proposed for investigation of branching random walks with a few sources. The results obtained may be useful for the investigations of the infections spread. The research was partially supported by RFBR grant 10-01-00266.

Finite two-queue systems where customers of each queue are the servers of the other queue. Speaker: Uri Yechiali, Tel Aviv University and Afeka College of Engineering, Israel. Co-authors: Efrat Perel.

We consider systems comprised of two interlacing ﬁnite queues where customers of each queue are the servers of the other queue. Denoting by Li the number of customers in queue i = 1, 2, we study three models: (i) Queue 1

(Q1) operates as a limited-buﬀer multi-server M(λ1)/M(µ1)/L2/max{0,N − L2} system, while queue 2 (Q2) operates as a limited-buﬀer single-server M(λ2)/M(µ2L1)/1/K − 1 queue. That is, at any moment, the L2 customers present in Q2 act as the servers of Q1, where service time of each individual customer is exponentially distributed with parameter µ1. The customers of Q2 are served by the L1 customers in Q1, who join hands together to form a single server with exponentially distributed service time of rate µ2L1. Arrivals to Qi follow a

Poisson process with rate λi. (ii) Q1 operates as in model (i), but Q2 operates as a limited buﬀer multi-server

133 M(λ2)/M(µ2)/L1/max{0,K − L1} system. (iii) Q1 is a limited buffer single-server M(λ1)/M(µ1L2)/1/N − 1 queue, while Q2 is an M(λ2)/M(µ2L1)/1/K − 1 queue. For each model we derive an implicit set of the (conditional) probability generating function of L1 (given L2), where, in model (iii), we obtain a set of differential equations rather than algebraic equations. Reformulating the models as finite QBD processes, we calculate the system’s steady state probabilities.

Generalizations of Wald’s lemma to stationary and ergodic point processes. Speaker: Michael Zazanis, Athens University of Economics and Business, Greece.

Using Campbell’s theorem, we obtain an expression for the expected forward recurrence time of a stationary and ergodic point process. This is used to derive a generalized form of Wald’s lemma that holds in the stationary and ergodic framework. We compare this result with existing generalizations of Wald’s lemma for Markov chains and discuss applications in stochastic simulation

An urn model for population mixing and the phases within. Speaker: Tong Zhang, George Washington University, USA. Co-authors: Hosam M. Mahmoud.

We introduce a generalization of the Ehrenfest urn model. In the generalized model, instead of drawing one or fixed number of balls at each time, random samples of independent identically distributed sizes with a general generating discrete distribution (the generator) are taken out of an urn containing white and blue balls. Each ball in the sample is repainted with the opposite color and the sample is replaced in the urn. We study the phases in the gradual change from the initial condition to the steady state. We look at the status of the urn after kn draws. We identify three phases of kn: The growing sublinear, the linear, and the superlinear. In the growing sublinear phase the number of white balls is normally distributed, with parameters that are influenced by the initial conditions and the generator. In the linear phase a different normal distribution applies, in which the influence of the initial conditions and the generator are attenuated. At the superlinear stage the mix is nearly perfect, with a nearly perfect symmetrical normal distribution in which the effect of the initial conditions and the generator is obliterated. We give interpretations for how the results in different phases conjoin at the “seam lines”. The Gaussian results are obtained via martingale theory. We give a few concrete examples.

On the crossing times of a one-dimensional diﬀusion process through two boundaries. Speaker: Cristina Zucca, Universit`adegli Studi di Torino, Italy. Co-authors: Laura Sacerdote.

In many applications one is interested in determining the distribution of the first passage time of a diffusion process, originated in x, through a constant boundary S1, knowing that the process has already crossed another constant boundary S2. To deal with this problem we study the joint distribution of the two random variables T1 and T2, first passage time of the diffusion process through the constant boundaries S1 and S2 respectively. Here

134 we focus on dependency properties of these two random variables making use of the copula notion. We consider both the instances x. We explicitly determine a closed for expression for the copula in the case of a Wiener process, while we propose a numerical approach for the case of an Ornstein-Uhlenbeck process.

135

Posters

Clustering integer-valued time series. Speaker: Andr´esM. Alonso, Universidad Carlos III de Madrid, Spain. Co-authors: Michael P. Wiper.

Time series clustering is an important area of research for diﬀerent disciplines. In seismology, Kakizawa, Shumway and Taniguchi (1998) apply cluster techniques in order to establish diﬀerences between classes of events such as earthquakes and mining explosions. Some published examples of cluster analysis in time series have been based on environmental data. See for instance Macchiato et al. (1995) for a spatial clustering of daily ambient temperature, Cowpertwait and Cox (1992) for an application to a rainfall problem, or Scotto et al. (2009) for sea-level heights analysis. Other examples can be found in medicine, economy, engineering, etcetera. Alonso et al. (2006) propose a dissimilarity measure based on comparing the full forecast densities associated to each series in the sample. In this paper, their clustering procedure is extended to cover the case of integer-valued models. Our approach uses a Bayesian procedure for obtaining the forecast probability distribution for each INAR–Poisson time series and then we use the symmetrized Kullback–Leibler divergence in order to evaluate the closeness of each pair of time series. The performance of the proposed procedure is illustrated with the intra–daily returns of the stocks listed in the IBEX35 index of the Madrid Stock Market.

Regions of controlled posterior risk. Speaker: Sandra Mar´ıaBargãoSaraiva Ferreira, Universidade da Beira Interior, Portugal. Co-authors: DárioFerreira, CéliaNunes, JoãoT. Mexia.

The aim of this paper is to show that Discriminant Analysis can be considered as a branch of Statistical Decision Theory when viewed from a Bayesian approach. Our work renders Discriminant Analysis more ﬂexible since it gives the possibility of classing an element as belonging to a group of populations. This possibility arises from the introduction of the concept of Regions of Controlled Posterior Risk.

A relation between the distributions of stopping time and stopped sum via Wald’s identity. Speaker: Michael Boutsikas, University of Piraeus, Greece. Co-authors: A.C. Rakitzis, D.L. Antzoulakos.

Let X1,X2, ... be a a sequence of independent random variables and let T be a stopping time associated with this sequence. By employing a special form of Wald’s identity we derive a relation between the probability gen- PT erating function (pgf) of T and the pgf or mgf of the stopped sum ST = i=1 Xi. This relation implies that, when the distribution of ST is known (for all probability measures derived after exponentially tilting the original probability measure), then the distribution of T is also known and vice versa. Two applications are offered in order to illustrate the applicability of our results. In the first one we consider a random walk Si, i = 1, 2, ..., with exponentially distributed positive or negative jumps and denote by T its first exit time from an interval

137 [−c, c]. By easily identifying the distribution of ST we manage to extract an exact formula for the pgf of the boundary crossing time T. In the second application we consider the case where Xi, i = 1, 2, ..., is a sequence of measurements taken from samples corresponding to lots of products of a manufacturing process (e.g. number of defective items in successive lots), and T is the waiting time until the sampling level of the inspection changes using a k/m scan (switching) rule associated with the sequence Xi, i = 1, 2, ... . Then, the joint pfg of T and

ST (e.g. total number of defective items observed) is obtained by exploiting the fact that T follows geometric distribution of order k/m.

Modeling rare events through a pRARMAX process. Speaker: Marta Ferreira, Universidade do Minho, Portugal. Co-authors: Luisa Canto e Castro.

In Ferreira and Canto e Castro (2008), a power max-autoregressive process (in short pARMAX) is presented as an alternative to heavy tailed ARMA when modeling rare events. Now we consider an extension of pARMAX by including a random component which makes the model more applicable to real data. We will see conditions under which this new model, here denoted as pRARMAX, has unique stationary distribution and we analyze its extremal behavior. Based on Bortot and Tawn (1998), we derive a threshold-dependent extremal index as a functional of the coeffcient of tail dependence of Ledford and Tawn (1996, 1997) which in turn relates with the pRARMAX parameter. In order to fit a pRARMAX model to an observed data series, we present a methodology based on minimizing the Bayes risk in classification theory and analyze this procedure through a simulation study. We illustrate with an application to financial data.

Chains of inﬁnite memory: what can we say without assuming continuity. Speaker: Alexsandro Gallo, Universidade Estadual de Campinas, Brazil.

For chains of inﬁnite memory (discrete time and countable alphabet) the state at time zero depends on the whole past of the chain. These are non-Markovian stochastic chains, and for this reason, the ”basic” questions are the following: does it exists a stationary measure for such chains? Is there a unique stationary measure? If yes, what are the statistical properties of this unique stationary measure?... To answer these questions, Doeblin and Fortet (1937) introduced the continuity assumption. In some sense, it is a way to ask the dependence to be very weak for on the remote past, and that in the limit, the state at time zero does not depends on the inﬁnitely remote states of the chain. Up to date, the whole literature has focussed on this continuity assumption. A natural question is to ask ”how much necessary” can be the continuity condition to answer the above questions. In this Poster, we present results that apply for the non-continuous case, providing a certain ”knowledge” about the discontinuity points.

Classiﬁcation of genomic sequences via wavelet variance and a self-organizing map with an

138 application to mitochondrial DNA. Speaker: Agnieszka Jach, Universidad Carlos III de Madrid, Spain. Co-authors: Juan Miguel Mar´ın.

We present a new methodology for discriminating genomic symbolic sequences, which combines wavelet analysis and a self-organizing map algorithm. Wavelets are used to extract variation across various scales in the oligonucleotide patterns of a sequence. The variation is quantified by the estimated wavelet variance, which yields a feature vector. Feature vectors obtained from many genomic sequences, possibly of different lengths, are then classified with a nonparametric self-organizing map scheme. When applied to nearly 200 entire mitochondrial DNA sequences, or their fragments, the method predicts species taxonomic group membership very well, and allows the results to be visualized. When only thousands of nucleotides are available, wavelet-based feature vectors of short oligonucleotide patterns are more efficient in discrimination than frequency-based feature vectors of long patterns. This new data analysis strategy could be extended to numeric genomic data. The routines needed to perform the computations are readily available in two packages of software R.

Multiscale entropy-based analysis of the eﬀect of deformation on intermittency. Speaker: Ana-Esther Madrid, Universidad de Granada, Spain. Co-authors: Jose Miguel Angulo.

Intermittency is a significant feature inherent to a wide variety of phenomena, and the analysis of its genesis, patterns and effects constitutes an important objective in many studies and applications, particularly in relation to control and risk assessment. From technical point of view, given the intrinsic nature of intermittency understood as the recurrent occurrence of events of a certain magnitude at a certain scale in the evolution of a random process, wavelets and related functions constitute a useful tool for mathematical description and analysis of such a behavior in terms of multiscale local energy distribution. Several indicators based on this approach have been proposed in this context. In this work, we analyze the effect of deformation of the process domain on intermittency characteristics, in terms of the implied inter- and intra-scale energy redistribution. Indicators based on both the Continuous Wavelet Transform (CWT) and the Discrete Wavelet Transform (DWT) are used to quantify intermittency levels. In particular, generalized entropy measures allow evaluating the distortion effect of deformation on the probabilistic structure of the process at different scales in relation to intermittency.

Limit theorems for a rumour process with random stiﬂing. Speaker: Pablo Mart´ın-Rodr´ıguez, University of S˜aoPaulo, Brazil. Co-authors: Elcio´ Lebensztayn, Fabio Prates Machado.

We propose a generalization for the Maki-Thompson rumour model by considering random stiﬂing. That this, we assume that a spreader does not decide to stop propagating the rumour until being involved in a random number of stiﬂing experiences. For this model we prove a Law of Large Numbers and a Central Limit Theorem for the proportion of the population never hearing the rumour.

139 Risk measures and stochastic orderings using the Lorenz curve. Speaker: Miguel Mendes, Universidade do Porto, Portugal. Co-authors: Ignacio Cascos.

We study the Generalized Lorenz curves of the minima of samples from a random variable. These Lorenz curves can be used to compare distributions in terms of their variability and deﬁne coherent risk measures. The dual Lorenz curves of the maxima of samples from the random variable are also considered.

Modelling extremal dependence in stock indices. Speaker: Alexandra Ramos, Universidade do Porto, Portugal. Co-authors: Anthony Ledford.

Recent advances in multivariate extreme value theory have led to improved techniques for characterizing the extremal behaviour of stationary time series. In particular, attention has been given to the within-cluster behaviour of the extremes of a series, which is determined by the short-range temporal dependence. Most of its characterization has been done based on the assumption of Markovianity of the time series, as the class of dth-order Markov chains is suﬃciently general and tractable.

We consider here joint tails of the distribution of two consecutive pairs (Xi,Xi+1) of a ﬁrst-order stationary Markov chain being modelled by the asymptotically motivated joint tail model described in Ramos and Ledford (2009). Applying this modelling approach to daily log-returns of stock indices, we examine both the upper and the lower joint tails, which requires the joint estimation of the extremal temporal dependence structure as well as the tail of the marginal distribution. In particular, we are interested in studying the strength of extremal dependence in both joint tails and the heaviness of the tails. We also examine the within-cluster behaviour of the extremes of the series by estimating the threshold dependent extremal index.

Robust inference in generalized linear models. Speaker: Isabel Rodrigues, Universidade T´ecnicade Lisboa, Portugal. Co-authors: Ana Bianco, Graciela Boente.

In many situations, data follow a generalized linear model in which the mean of the responses is modeled, through a link function, linearly on the covariates. In this paper, robust estimators for the regression parameter are considered in order to build test statistics for this parameter. We derive the asymptotic behavior of the robust estimators for the regression parameter under the null hypothesis and under contiguous alternatives in order to obtain that of the robust Wald test statistic.

Goodness-of-ﬁt test for density estimation with directional data. Speaker: Daniela Rodr´ıguez, Universidad de Buenos Aires, Argentina. Co-authors: Wenceslao Gonzalez-Manteiga.

In this work, we study the problem of testing the hypothesis whether the density f of a random variable on a

140 sphere belongs to a given class of densities. We propose a test statistic and we derive its asymptotic properties. We also considered a bootstrap procedure to approximate the distribution of the test statistic. Through a simulation study, we explored the performance of the test procedure under the null hypothesis and under diﬀerent alternatives. We illustrate the test procedure on a real data.

Testing ﬁt for grouped circular data. Speaker: Zheng Sun, Simon Fraser University, Canada.

Watson’s U 2 statistic for testing fit to a distribution around a circle with continuous data, is here adapted for use with grouped data. Such data arises often in biological experiment and in other areas of science where angles can not be measured very accurately. For example, the directions taken by homing birds might be measured only to the nearest 10 degrees and the data given consists of counts in cells of width 10 degrees around a circle. Suppose a parametric continuous distribution is fitted to such data. Maximum likelihood is used to estimate the parameters and therefore the expected values in each cell can be calculated. The grouped version of Watson’s statistic compares the cumulative histogram of the observations with the cumulative histogram of the expected values. It is shown to how to find the asymptotic distribution of the statistic and hence to find the p-value of the sample. Monte Carlo studies show that this gives an excellent approximation to the finite-n p-value. Watson’s statistic has advantages over Pearson’s X2: it avoids the problem of small expected values, and it is generally more powerful than the X2 statistic. Even continuous data is effective grouped by the accuracy of measurement. There are some advantages in treating such data as grouped. The above methods will be demonstrated on several data sets.

Poisson approximation of the mixed Poisson distribution with inﬁnitely divisible mixing law. Speaker: Eﬃe Vaggelatou, University of Athens, Greece.

In this work, explicit upper bounds are provided for the Kolmogorov and total variation distances between the mixed Poisson distribution with inﬁnitely divisible mixing law and the Poisson distribution. If µ and σ2 are the mean and variance of the mixing distribution respectively, then the bounds provided here are asymptotically equal √ √ to σ2/(2µ 2πe) and σ2/(µ 2πe) for the Kolmogorov and the total variation distance respectively when µ → ∞ and σ2 is ﬁxed. Finally, as an application, the Poisson approximation of the negative Binomial distribution is considered.

141

Authors Index

A Bibbona, Enrico, 99 Abbas, Karim, 97 Biermé,Hermine, 100 Abd-Elfattah, Abdallah Mohamed, 97 Biffis, Enrico, 41 Aguilera, Ana M., 35 Birmelé,Etienne, 40 Al-Motairi, Hessah, 97 Boente, Graciela, 100 Alonso, AndrésM., 137 Boistard, Hélène,41 Alonso, Francisco Javier, 35 Boogaart, K. Gerald van den, 41 Alonso González,Pablo, 97 Borovkov, Konstantin, 100 Altendorf, Hellen, 35 Boudaren, Mohamed El Yazid, 101 Alvarez´ Esteban, Pedro César, 36 Boutsikas, Michael, 137 Aoshima, Makoto, 36 Brodsky, Boris, 42 Arribas Gil, Ana, 37 Broniatowski, Michel, 101 Aston, John, 37 Bulinskaya, Ekaterina, 102 Atar, Rami, 37 Bunouf, Pierre, 42 Avram, Florin, 98 Aza¨ıs,Jean-Marc, 38 C Cabaña,Enrique M., 43 B Calderhead, Ben, 43 Badagián, Ana Laura, 98 Calka, Pierre, 43 Balbás, Raquel, 98 Cañada-Jaime, Héctor, 44 Barbu, Vlad Stefan, 38 Capasso, Vincenzo, 102 BargãoSaraiva Ferreira, Sandra Mar´ıa,137 Cárcamo,Javier, 44 Barrio, Eustasio del, 38 Carlier, Guillaume, 44 Barrios, Juan M., 98 Cascos, Ignacio, 44 Behrens, Sarah, 38 Cérou,Frédéric,45 Belzunce, Félix,39 Ceyhan, Elvan, 103 Benes, Viktor, 99 Chacón,JoséE., 103 Bérard, Jean, 39 Chan, Hock Peng, 45 Berrendero, JoséR., 39 Chapman, Sandra, 103 Beskos, Alexandros, 40 Chen, Haiyan, 45 Biard, Romain, 40 Chen, Jie, 46 Biase, Giuseppe Di, 99 Chen, Nan, 46 Biau, Gérard, 40 Cheridito, Patrick, 47

143 Christakos, George, 47 Fraiman, Ricardo, 31 Chronopoulou, Alexandra, 104 Franco, Manuel, 110 Cirillo, Pasquale, 104 Franco Pereira, Alba Mar´ıa,110 Clancy, Damian, 105 Frostig, Esther, 53 Claramunt, M. Mercè,47 Fu, James C., 53 Corcuera, JoséManuel, 105 Fuentes, Montserrat, 31 Crescenzo, Antonio Di, 105 Crimaldi, Irene, 106 G Cruz-Orive, Luis M., 48 Gago-Ben´ıtez,Ana, 110 Gallo, Alexsandro, 138 Cuesta-Albertos , Juan A., 48 Galtchouk, Leonid, 54 Cuevas, Antonio, 48 Garcia, Nancy, 111 Czechowski, Zbigniew, 49 Garrido, José,54 D Gathy, Maude, 111 D’Amico, Guglielmo, 49 Genton, Marc, 54 D’Auria, Bernardo, 49 Ginebra, Josep, 54 Dabala, Wieslawa, 106 Glavan, Silviu, 55 Darkhovsky, Boris, 50 Glaz, Joseph, 55 Dayanik, Savas, 50 Goegebeur, Yuri, 55 Deheuvels, Paul, 50 Gomes, Mar´ıaIvette, 56 Dhersin, Jean-Stéphane,51 Gon¸calves,Ana Patricia, 56 Diko, Peter, 107 Gosh, Arka, 112 Gregorio, Alessandro De, 112 E Guerin, Fabrice, 56 Eleftheriou, Mavroudis, 107 Guillas, Serge, 57 Eliazar, Iddo, 107 Guillou, Armelle, 113 Eliazar, Iddo, 51 Gulati, Sneh, 113 Embrechts, Paul, 31 Guo, Jiqiang, 57 Eryilmaz, Serkan, 51 Gupta, Rahul, 114 Escudero, Laureano, 108 Gurvich, Itai, 57 Esteban, Mercedes, 52 Guyader, Arnaud, 57 Estrade, Anne, 109 H F Hadjikyriakou, Milto, 114 Feinberg, Eugene, 109 Hadjiliadis, Olympia, 58 Fellouris, Georgios, 52 Haiman, George, 58 Ferreira, Marta, 138 Halim, Zeghdoudi, 115 Fiems, Dieter, 109 Hautphenne, Sophie, 115 Figueroa-López, José,52 Heinrich, Lothar, 58 Fouladirad, Mitra, 52 Hernández-del-Valle , Gerardo, 59

144 Hinz, Juri, 115 Loh, Ji Meng, 67 Hochberg, Kenneth, 59 Loisel, Stéphane,67 Holmes, Susan, 59 Lon, Polly, 119 LondoñoLondoño,Jaime Alberto, 119 I López, F. Javier, 119 Ikeda, Satoshi, 60 López-D´ıaz,Miguel, 67 J Lopker, Andreas H., 68 Jach, Agnieszka, 139 Lou, Wendy, 68 Jacko, Peter, 115 Ludeña,Carenne, 68 Jacob, Christine, 60 Lundgren, Robin, 119 Jiménez,Raúl,60 Luque-Vásquez,Fernando, 69 Johnson, Brad C., 61 M K Machado, Fábio,69 Kabluchko, Zakhar, 61 Madrid, Ana-Esther, 139 Kaishev, Vladimir, 61 Mah, Olivia, 120 Kalogeropoulos, Konstantinos, 116 Mahmoud, Hosam M., 69 Kalpathy, Ravi, 116 Manca, Raimondo, 70 Kessler, Mathieu, 62 Markus, Laszlo, 70 Khaledi, Baha-Eldin, 62 Mart´ın-Rodr´ıguez,Pablo, 139 Kimmel, Marek, 63 Martin, Donald E. K., 70 Kokonendji, CélestinC., 63 Matalliotakis, George, 71 Kontoyiannis, Ioannis, 63 Mateu, Jorge, 71 Kortschak, Dominik, 116 Meinguet, Thomas, 120 Kovalenko, Andrey, 117 Mendes, Miguel, 140 Méndez-Salazar, Marco A., 72 L Molchanov, Ilya, 72 Lachal, Aimé,64 Morale, Daniela, 121 Lai, Lifeng, 64 Mosler, Karl, 121 Laniado Rodas, Henry, 117 Mukherjee, Amitava, 72 Latuszynski, Krzysztof, 65 Mukhopadhyay, Nitis, 72 Ledoux, James, 117 Mulero, Julio, 121 Lefèvre,Claude, 65 Müller,Alfred, 73 Lelarge, Marc, 65 Leskelä,Lasse, 118 N Leung, Ming-Ying, 65 Navarro, Jorge, 73 Li, Xiaohu, 66 Neill, Daniel, 73 Lian, Heng, 66 Nguyen, Giang, 122 Lieshout, Marie-Colette van, 66 Nikiforov, Igor, 74 Lochowski, Rafal, 118 Novales, Alfonso, 74

145 O Rodrigues, Isabel, 140 Oprisan, Adina, 75 Rodr´ıguez, Daniela, 140 Orsingher, Enzo, 75 Rodr´ıguez-Griñolo,Rosario, 125 Ortega, Eva Mar´ıa,122 Rosco, Juan Francisco, 126 Ortega, Isabel, 123 Rotondi, Renata, 82 Ortega, Joaqu´ın,123 Rubinstein, Reuven, 82 Ruggiero, Matteo, 83 P Runggaldier, Wolfgang, 83 Pacheco, António, 75 Panholzer, Alois, 76 S Papadopoulou, Aleka, 124 Sacerdote, Laura, 126 Papapantoleon, Antonis, 76 Scarsini, Marco, 83 Pateiro-López, Beatriz, 76 Schreiber, Tomasz, 126 Pemantle, Robin, 32 Segovia, Maria del Carmen, 127 Peña,Victor de la, 32 Shaked, Moshe, 83 Perry, David, 77 Shao, Yongzhao, 84 Perry, Ohad, 77 Sirl, David, 127 Petroni, Filippo, 77 Skiadas, Christos H., 84 Pievatolo, Antonio, 78 Sordo, Miguel Angel,´ 84 Politis, Konstadinos, 78 Spodarev, Evgeny, 84 Pospisil, Libor, 78 Steele, J. Michael, 32 Preda, Cristian, 79 Steland, Ansgar, 127 Prieto-Rumeau, Tomás,79 Stephens, Michael, 85 Prokesova, Michaela, 79 Stewart, Michael, 85 Puerto, InésMar´ıadel, 80 Suárez-Llorens, Alfonso, 85 Sucarrat, Genaro, 128 R Sun, Zheng, 141 Ramalhoto, M. F., 124 Swan, Yvik, 128 Ram´ırez-Cobo, Pepa, 124 Szatzschneider, Wojciech, 85 Ramos, Alexandra, 140 Rao, M. B., 124 T Redenbach, Claudia, 80 Tartakovsky, Alexander, 86 Reis, Paula, 125 Tchamkerten, Aslan, 86 Renaud, Jean-Fran¸cois,125 Temido, Maria da Gra¸ca,129 Renom, JoséM., 80 Thiedmann, Ralf, 87 Resing, Jacques, 81 Thomson, Peter, 87 Reuveni, Shlomi, 81 Toninelli, Cristina, 88 Rinott, Yosef, 81 Torrado, Nuria, 88 Robert, Christian-Yann, 81 Trandafir, Paula Camelia, 129 Robin, Stéphane,82 Trufin, Julien, 88

146 Turck, Koen De, 129 Zuyev, Sergei, 95 Zwart, Bert, 96 V Vaggelatou, Eﬃe, 141 Valsero Blanco, Mar´ıaCruz, 130 Vardoulaki, Maria, 89 Varini, Elisa, 89 Vasiliadis, George, 130 Vecer, Jan, 90 Veen, Alejandro, 131 Veeravalli, Venugopal, 90 Velasco, Carlos, 90 Villar, Soﬁa Soledad, 131 Vlasiou, Maria, 91 Voss, Florian, 91 Votsi, Irene, 132

W Ward, Amy, 92 Ward, Mark Daniel, 92 Watkins, Nicholas, 92 Wijk, Sandra (A.C.C.) van, 132 Wiper, Michael, 93 Wugalter, Alexander, 93 Wu, Zhengxiao, 132

Y Yamazaki, Kazutoshi, 133 Yarovaya, Elena, 133 Yata, Kazuyoshi, 94 Yechiali, Uri, 133 Yu, Yaming, 94

Z Zacks, Shelemyahu, 94 Zazanis, Michael, 134 Zervos, Mihail, 33 Zhang, Tong, 134 Zheng, Rong, 95 Zhu, Zhengyuan, 95 Zucca, Cristina, 134

147 148