Concentrated Advanced Course January 7-8, 1999 and Workshop January 11-13, 1999 on Pro duct Integrals and Pathwise Integration Foreword In the week January 7-13, 1999 a course and a workshop on Product Integrals and Path- wise Integration was held by MaPhySto at the Department of Mathematical Sciences, University of Aarhus. The course and workshop was organized by Ole E. Barndor -Nielsen Aarhus, Denmark, Svend Erik Graversen Aarhus, Denmark and Thomas Mikosch Groningen, The Nether- lands. In this lea et we have gathered the program, the list of participants and the workshop abstracts. The notes for the course app eared as the rst volume of the MaPhySto Lecture Notes series and may be fetched from our web-site www.maphysto.dk; hardcopies may also b e ordered. Contents 1 Course Program 2 2 Workshop Program 3 3 Combined list of participants to the Course and to the Workshop 5 4 Abstracts 12 1 Course Program Thursday January 7 R. Dudley: How should integrals of Stieltjes type be de ned? . 9.30-10.30 Coffee/tea R. Norvaisa: Stochastic integrals . 10.50-11.50 R. Dudley: Lyons' work on obstacles to pathwise It^o integration. 12.00-12.30 Lunch 12.30-13.30 R. Dudley: Di erentiability with respect to p-variation norms I. 13.30-14.15 R. Dudley: Di erentiability with respect to p-variation norms II. 14.20-15.05 Coffee/tea R. Norvaisa: Properties of p-variation I. 15.20-16.00 R. Norvaisa: Properties of p-variation II. 16.15-17.00 Friday January 8 R. Norvaisa: Stochastic processes and p-variation. 9.30-10.30 Coffee/tea R. Dudley: Empirical processes and p-variation. 10.45-11.45 Lunch 12.00-13.00 R. Norvaisa: Integration. 13.00-14.00 R. Dudley: Ordinary di erential equations and product integrals. 14.10-14.40 Coffee/tea R. Norvaisa: Product integrals. 15.00-16.00 R. Dudley: Other aspects of product integrals. 16.10-16.40 2 2 Workshop Program Monday January 11 Registration and coffee/tea 09.30-10.00 Chairman: Thomas Mikosch Ole E. Barndor -Nielsen and Thomas Mikosch: 10.00-10.10 Introduction. Richard Gill: Product-integration and its applications in survival 10.10-11.00 analysis. Norb ert Hofmann: Optimal Pathwise Approximation of Stochas- 11.10-12.00 tic Di erential Equations. Lunch 12.00-14.00 Chairman: Svend Erik Graversen EskoValkeila: Some maximal inequalities for fractional Brownian 14.00-14.30 motions. Richard Dudley: On Terry Lyons's work. 14.35-15.25 Coffee/tea Rimas Norvaisa: p-variation and integration of sample functions 16.00-16.50 of stochastic processes. Sren Asmussen: Martingales for re ected Markov additive pro- 17.00-17.50 cesses via stochastic integration. Tuesday January 12 Chairman: Jrgen Ho mann-Jrgensen Philipp e Carmona: Stochastic integration with respect to frac- 09.00-09.40 tional Brownian motion. Rama Cont: Econometrics without probability: measuring the 09.45-10.35 pathwise regularity of price trajectories. Coffee/tea Francesco Russo: Calculus with respect to a nite quadratic 11.00-11.50 variation process. Lunch 12.00-14.00 3 Chairman: Sren Asmussen Pierre Vallois: Stochastic calculus related to general Gaussian 14.00-14.50 processes and normal martingales. Imme van den Berg: Stochastic di erence equations, discrete 14.55-15.45 Fokker-Planck equation and nite path-integral solutions. Coffee/tea Rudolf Grub el: Di erentiability properties of some classical 16.10-17.00 stochastic models. Donna M. Salop ek: When is the stop-loss start gain strategy 17.05-17.45 self- nancing?. Discussion 17.50-18.30 Wednesday January 13 Chairman: Ole E. Barndor -Nielsen Bo Markussen: Graphical representation of interacting particle 09.00-09.40 systems. Jan Rosinski: Independenceof multiple stochastic integrals. 09.45-10.35 Coffee/tea Zbigniew J. Jurek: In nite divisibility revisited. 11.00-11.50 Lunch 12.00-14.00 4 3 Combined list of participants to the Course and to the Workshop Sren Asmussen Department of Mathematical Statistics University of Lund Box 118 S-221 00 Lund, Sweden Email: [email protected] Ole E. Barndor -Nielsen Department of Mathematical Sciences Theoretical Statistics University of Aarhus DK-8000 Aarhus C, Denmark Email: o [email protected] Jo chen Beisser Chair of Banking University of Mainz Jakob Welder-Weg 9 D-55099 Mainz, Germany Email: b [email protected] Fred Esp en Benth Department of Mathematical Sciences Theoretical Statistics University of Aarhus DK-8000 Aarhus C, Denmark Email: [email protected] Preb en Blsild Department of Mathematical Sciences Theoretical Statistics University of Aarhus DK-8000 Aarhus C, Denmark Email: preb [email protected] Philipp e Carmona Lab oratoire de Statistique et Probabilit es Universit ePaul Sabatier 118 Route de Narb onne 31062 Toulouse Cedex, France 5 Email: [email protected] Rama Cont Centre de Mathematiques Appliquees CNRS-Ecole Polytechnique CMAP - Ecole Polytechnique F-91128 Palaiseau, France Email: Rama.Cont@p olytechnique.fr Richard M. Dudley MIT - Departmentof Mathematics Ro om 2-245 Cambridge, MA 02139 U.S.A. Email: [email protected] Sren Fournais Department of Mathematical Sciences University of Aarhus DK-8000 Aarhus C Denmark Email: [email protected] Dario Gasbarra Rolf Nevanlinna Institute University of Helsinki PL 4 00014 Helsinki Finland Email: [email protected]. Richard D. Gill University of Utrecht Mathematical Institute Budap estlaan 6 NL-3584 CD Utrecht, The Netherlands Email: [email protected] Svend Erik Graversen Department of Mathematical Sciences Theoretical Statistics University of Aarhus DK-8000 Aarhus, Denmark Email: [email protected] 6 Rudolf Grub el Universitat Hannover FB Matematik Welfengarten 1, PF 60 09 D-30617 Hannover, Germany Email: rgrub el@sto chastik.uni-hannover.de Sren Kold Hansen Department of Mathematical Sciences University of Aarhus DK-8000 Aarhus C Denmark Email: [email protected] Norb ert Hofman Mathematisches Institut Universitat Erlangen-Nurn b erg Bismarckstr. 1 1/2 91054 Erlangen, Germany Email: [email protected] Jrgen Ho mann-Jrgensen Department of Mathematical Sciences Theoretical Statistics University of Aarhus DK-8000 Aarhus C, Denmark Email: ho @imf.au.dk Per Horfelt Dept. of Mathematics Chalmers University of Technology Goteb org University SE-412 96 Goteb org, Sweden Email: p [email protected] EvaVedel Jensen Department of Mathematical Sciences Theoretical Statistics University of Aarhus DK-8000 Aarhus C, Denmark Email: [email protected] Jens Ledet Jensen Department of Mathematical Sciences 7 Theoretical Statistics University of Aarhus DK-8000 Aarhus C, Denmark Email: [email protected] Wenjiang Jiang Department of Mathematical Sciences University of Aarhus DK-8000 Aarhus C Denmark Email: [email protected] Zbigniew J. Jurek Institute of Mathematics University of Wro claw Pl. Grunwaldzki 2/4 50-384 Wro claw, Poland Email: [email protected] c.pl Marie Kratz Universite Paris V U.F.R. Maths/Info. 45 rue des Saints-Peres 75270 cedex 6Paris, France Email: [email protected] Martynas Manstavicius Department of Mathematics Vilnius University Naugarduko LT-2006 Vilnius, Lithuania Email: [email protected] Bo Markussen Inst. for Matematiske Fag Kb enhavns Universitet Universitetsparken 5 2100 Kb enhavn , Danmark Email: [email protected] Thomas Mikosch RUG Groningen Faculty of Mathematics and Physics PO Box 800 8 NL-9700 AV Groningen, The Netherlands Email: [email protected] Elisa Nicolato Department of Mathematical Sciences Theoretical Statistics University of Aarhus DK-8000 Aarhus C, Denmark Email: [email protected] Rimas Norvaisa Institute of Mathematics and Informatics Akademijos 4 2600 Vilnius Lithuania Email: [email protected] Jan Parner Biostatistisk Afdeling Panum Instituttet Blegdamsvej 3 1 b enhavn N, Denmark DK-2200 K 2 Email: [email protected] Jan Pedersen Department of Mathematical Sciences Theoretical Statistics University of Aarhus DK-8000 Aarhus C, Denmark Email: [email protected] Jacob Krabb e Pedersen Department of Mathematical Sciences Theoretical Statistics University of Aarhus DK-8000 Aarhus C, Denmark Email: krabb [email protected] Goran Peskir Department of Mathematical Sciences Theoretical Statistics University of Aarhus DK-8000 Aarhus C, Denmark Email: [email protected] 9 Karsten Prause Institut fur Mathematische Sto chastik Universitt Freiburg Eckerstrasse 1 D-79104 Freiburg, Germany Email: [email protected] Jan Ros nski Department of Mathematics 121 Ayres Hall University of Tennessee Knoxville, TN 37996-1300, U.S.A. Email: [email protected] Francesco Russo Universit eParis XIII Institut Galil ee, Math ematiques Av. Jean-Baptiste Cl ement F-93430 Villetaneuse, France Email: [email protected] Donna M. Salop ek Dept. of Mathematics P.O.Box 800 University of Groningen NL-9700 Av Groningen, The Netherlands Email: [email protected] Ken-iti Sato Hachimanayama 1101-5-103 Tenpaku-ku Nagoya 468-0074 Japan Email: Hansp eter Schmidli Department of Mathematical Sciences Theoretical Statistics University of Aarhus DK-8000 Aarhus C, Denmark Email: A. Reza Soltani 10 College of Sciences Shiraz University Shiraz Iran Email: [email protected] Tommi Sottinen Department of Mathematics University of Helsinki P.O. Box 4 FIN-00014 Email: tsottine@ro ck.helsinki. Esko Valkeila Compting Centre University of Helsinki P.O. Box 26 00014 Helsinki Finland Email: [email protected]. Pierre Vallois Universit ede Nancy 1 D epartementde Math ematiques B.P. 239 F-54506 Vanduvre les Nancy Cedex France Email: [email protected] Imme van den Berg Department of econometrics University of Groningen P.O.Box 800 9700 AV Groningen, The Netherlands Email: [email protected] Allan Wurtz Dept. of Economics University of Aarhus DK-8000 Aarhus C Denmark Email: [email protected] 11 4 Abstracts On the following pages you will nd the extended abstracts submitted to the organizers.