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9<HTMERB=Ehijdf> News 6/2013 Mathematics C. Abbas, Michigan State University, East Lansing, K. Alladi, University of Florida, Gainesville, FL, T. Aven, University of Oslo, Norway; U. Jensen, MI, USA USA; P. Paule, Johannes Kepler University Linz, University of Hohenheim, Germany Austria; J. Sellers, A. J. Yee, The Pennsylvania State Introduction to Compactness University, University Park, PA, USA (Eds) Stochastic Models in Reliability Results in Symplectic Field Combinatory Analysis This book provides a comprehensive up-to-date Theory presentation of some of the classical areas of reli- Dedicated to George Andrews ability, based on a more advanced probabilistic framework using the modern theory of stochastic The book grew out of lectures given by the Contents author in 2005. Symplectic field theory is a processes. This framework allows analysts to for- Congruences modulo powers of 2 for a certain new important subject which is currently being mulate general failure models, establish formulae partition function (H.-C. Chan and S. Cooper).- developed. The starting point of this theory are for computing various performance measures, Cranks—really, the final problem (B.C. Berndt, compactness results for holomorphic curves as well as determine how to identify optimal H.H. Chan, S.H. Chan, and W.-C. Liaw).- Eisen- established in 2004. The book gives a systematic replacement policies in complex situations. In stein series and Ramanujan-type series for 1/π introduction providing a lot of background mate- this second edition of the book, two major topics (N.D. Baruah and B.C. Berndt).- Parity in parti- rial much of which is scattered throughout the have been added to the original version: copula tion identities (G.E. Andrews).- Some combina- literature. The aim is to provide an entry point into models which are used to study the effect of torial properties of hook lengths, contents, and symplectic field theory for non-specialists and for structural dependencies on the system reliability; parts of partitions (R.P. Stanley).- The doubloon graduate students. In addition, the book provides and maintenance optimization which highlights polynomial triangle (D. Foata and G.-N. Han).- extensions of certain compactness results which delay time models under safety constraints. Terje Hook lengths and shifted parts of partitions (G.-N. are believed to be true by the specialists but which Aven is Professor of Reliability and Risk Analysis Han).- A unification of two refinements of Eluer’s have not yet been published in the literature in at University of Stavanger, Norway. Uwe Jensen is partition theorem (W.Y.C. Chen, H.Y. Gao, K.Q. detail. working as a Professor at the Institute of Applied Ji, and M.Y.X. Li).- Identities and congruences for Mathematics and Statistics of the University of Rajamnujan’s ω(q) (J.H. Bruinier and K. Ono).- Features Hohenheim in Stuttgart, Germany. Review of first On the subpartitions of the ordinary partitions 7 Systematic introduction into compactness edition: “This is an excellent book on mathemati- (B. Kim).- Arithmetic properties of partitions results for holomorphic curves 7 Entry point cal, statistical and stochastic models in reliability. with even parts distinct (G.E. Andrews, M.D. into symplectic field theory for non-specialists The authors have done an excellent job of unifying Hirschhorn, and J.A. Sellers).- Modularity and the and students 7 Extensions to some compactness some of the stochastic models in reliability. results not yet published distinct rank function (A. Folsom).- Cluster parity indices of partitions (K. Kurşungöz).- Ramanujan’s Features Fields of interest partial theta series and parity in partitions (A.J. 7 Unifies some of the stochastic models in Differential Geometry; Manifolds and Cell Com- Yee).- A combinatorial study and comparison of reliability 7 Reference book for researchers in plexes (incl. Diff.Topology) partial theta identities of Andrews and Ramanujan reliability mathematics 7 A comprehensive up- (K. Alladi).- New identities involving sums of the to-date presentation of some of the classical areas Target groups tails related to real quadratic fields (K. Bringmann of reliability Research and B. Kane).- Rademacher-type formulas for restricted partition and overpartition functions Contents Discount group (A.V. Sills).- Bijective proofs using two-line matrix Introduction.- Basic Reliability Theory.- Stochastic Professional Non-Medical representations for partitions (E.H.M. Brietzke, Failure Models.- Availability Analysis of Complex J.P.O. Santos, and R. da Silva).- Balanced partitions Systems.- Maintenance Optimization. (S. Vandervelde).- Partitions with rounded occur- rences and attached parts (J. Lovejoy). [...] Fields of interest Probability Theory and Stochastic Processes; Fields of interest Quality Control, Reliability, Safety and Risk; Op- Number Theory; Analysis; Algebra erations Research, Management Science Target groups Target groups Research Research Discount group Discount group Professional Non-Medical Professional Non-Medical Due June 2013 Only available in print Due August 2013 Due June 2013 2013. VIII, 422 p. (Developments in Mathematics, 2nd ed. 2013. X, 310 p. (Stochastic Modelling and 2013. X, 200 p. Hardcover Volume 32) Hardcover Applied Probability, Volume 41) Hardcover 7 approx. $119.00 7 $129.00 7 $129.00 ISBN 978-3-642-31542-8 ISBN 978-1-4614-7857-7 ISBN 978-1-4614-7893-5 9<HTOGPC=dbfeci> 9<HTMERB=ehifhh> 9<HTMERB=ehijdf> 59 Mathematics springer.com/NEWSonline D. Bakry, Université Paul Sabatier, Toulouse, J. Baldeaux, E. Platen, University of Technology L. Barreira, Universidade Técnica de Lisboa, Portugal France; I. Gentil, Université Claude Bernard Lyon 1, Sydney, Haymarket, NSW, Australia Dimension Theory of Villeurbanne, France; M. Ledoux, Université Paul Functionals of Sabatier, Toulouse, France Hyperbolic Flows Multidimensional Diffusions Analysis and Geometry of The dimension theory of dynamical systems has Markov Diffusion Operators with Applications to Finance progressively developed, especially over the last two decades, into an independent and extremely Features The present volume is an extensive monograph active field of research. Its main aim is to study the 7 Provides the reader in a systematic way with on the analytic and geometric aspects of Markov complexity of sets and measures that are invariant the ability to derive explicit formulas for function- diffusion operators. under the dynamics. In particular, it is essential to als of multidimensional diffusions 7 Special characterizing chaotic strange attractors. To date, unique chapters on Lie symmetry group methods Features some parts of the theory have either only been and matrix valued Wishart processes 7 Provides 7 First book to give systematic account of the outlined, because they can be reduced to the case the most recent introduction to the benchmark rich interplay between analytic, probabilistic of maps, or are too technical for a wider audience. approach to finance pioneered by Platen and and geometric aspects of Markov diffusion In this respect, the present monograph is intended co-authors 7 The reader finds readily applicable operators 7 Authors are leading players in the to provide a comprehensive guide. Moreover, exact simulation methods for various multidimen- field 7 Covers large body of results and tech- the text is self-contained and with the exception sional diffusion processes niques from the early developments to the current of some basic results in Chapters 3 and 4, all the achievements Contents results in the book include detailed proofs. The book is intended for researchers and graduate Contents 1 A Benchmark Approach to Risk Management.- 2 students specializing in dynamical systems who Introduction.- Part I Markov semigroups, basics Functionals of Wiener Processes.- 3 Functionals of wish to have a sufficiently comprehensive view of and examples: 1.Markov semigroups.- 2.Model Squared Bessel Processes.- 4 Lie Symmetry Group the theory together with a working knowledge of examples.- 3.General setting.- Part II Three model Methods.- 5 Transition Densities via Lie Symme- its main techniques. functional inequalities: 4.Poincaré inequali- try Methods.- 6 Exact and Almost Exact Simula- ties.- 5.Logarithmic Sobolev inequalities.- 6.So- tion.- 7 Affine Diffusion Processes on the Euclid- Features ean Space.- 8 Pricing Using Affine Diffusions.- 9 bolev inequalities.- Part III Related functional, 7 First comprehensive exposition of dimen- Solvable Affine Processes on the Euclidean State isoperimetric and transportation inequalities: sion theory of hyperbolic flows 7 Includes an Space.- 10 An Introduction to Matrix Variate Sto- 7.Generalized functional inequalities.- 8.Capacity overview of dimension theory and multifractal chastics.- 11 Wishart Processes.- 12 Monte Carlo and isoperimetry-type inequalities.- 9.Optimal analysis 7 Includes a detailed discussion of and Quasi-Monte Carlo Methods.- 13 Computa- transportation and functional inequalities.- Part major open problems in the area IV Appendices: A.Semigroups of bounded opera- tional Tools.- 14 Credit Risk under the Benchmark tors on a Banach space.- B.Elements of stochastic Approach.- A Continuous Stochastic Processes.- B Contents calculus.- C.Some basic notions in differential Time-Homogeneous Scalar Diffusions.- C Detect- Introduction.- Suspension Flows.- Hyperbolic and Riemannian geometry.- Notations and list of ing Strict Local Martingales. Flows.- Pressure and Dimension.- Dimension symbols.- Bibliography.- Index. of Hyperbolic Sets.- Pointwise
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