Springer albeverio s schachermayer w talagrand m lectures on probability theory and etatistics 30 lecs st flour 2000 (lnm 1816 springer 2003)(isbn 3540403353)(303s)

Lecture Notes in Mathematics Editors: J. M Morel, Cachan F Takens, Groningen B Teissier, Paris 1816 Berlin Heidelberg New York Hong Kong London Milan Paris Tokyo S Albeverio W Schachermayer M Talagrand Lectures on Probability Theory and Statistics Ecole d’Et´e de Probabilit´es de Saint-Flour XXX - 2000 Editor: Pierre Bernard 13 Authors Editor Sergio Albeverio Institute for Applied Mathematics, Probability Theory and Statistics University of Bonn Wegelerstr 53115 Bonn, Germany Pierre Bernard Laboratoire de Math´ematiques Appliqu´ees UMR CNRS 6620, Universit´e Blaise Pascal Clermont-Ferrand, 63177 Aubi`ere Cedex France e-mail: pierre.bernard@math.univ-bpclermont.fr e-mail: albeverio@uni-bonn.de Walter Schachermayer Department of Financial and Actuarial Mathematics Vienna University of Technology Wiedner Hauptstraße 10/105 1040 Vienna, Austria e-mail: wschach@fam.tuwien.ac.at Michel Talagrand Equipe d’Analyse Universit´e Paris VI Place Jussieu 75230 Paris Cedex 05 France e-mail: mit@ccr.jussieu.fr Cover: Blaise Pascal (1623-1662) Cataloging-in-Publication Data applied for Bibliographic information published by Die Deutsche Bibliothek Die Deutsche Bibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data is available in the Internet at http://dnb.ddb.de Mathematics Subject Classification (2000): 60-01, 60-06, 60G05, 60G60, 60J35, 60J45, 60J60, 70-01, 81-06, 81T08, 82-01, 82B44, 82D30, 90-01, 90A09 ISSN 0075-8434 Lecture Notes in Mathematics ISSN 0721-5363 Ecole d’Et´e des Probabilit´es de St Flour ISBN 3-540-40335-3 Springer-Verlag Berlin Heidelberg New York This work is subject to copyright All rights are reserved, whether the whole or part of the material is concerned, specif ically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microf ilm or in any other way, and storage in data banks Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer-Verlag Violations are liable for prosecution under the German Copyright Law Springer-Verlag Berlin Heidelberg New York a member of BertelsmannSpringer Science + Business Media GmbH http://www.springer.de c Springer-Verlag Berlin Heidelberg 2003 Printed in Germany The use of general descriptive names, registered names, trademarks, etc in this publication does not imply, even in the absence of a specif ic statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use Typesetting: Camera-ready TEX output by the authors SPIN: 10931677 41/3142/du - 543210 - Printed on acid-free paper INTRODUCTION This volume contains lectures given at the Saint-Flour Summer School of Probability Theory during the period August 17th - September 3d, 2000 This school was Summer School 2000 of the European Mathematical Society We thank the authors for all the hard work they accomplished Their lectures are a work of reference in their domain The School brought together 90 participants, 39 of whom gave a lecture concerning their research work At the end of this volume you will find the list of participants and their papers Thanks We thank the European Math Society, the European Commission DG12, Blaise Pascal University, the CNRS, the UNESCO, the city of SaintFlour, the department of Cantal, the Region of Auvergne for their helps and sponsoring Finally, to facilitate research concerning previous schools we give here the number of the volume of “Lecture Notes” where they can be found: Lecture Notes in Mathematics 1971 1976 1980 1984 1989 1993 1997 : : : : : : : no no no no no no no 307 – 1973 : no 390 – 1974 : no 480 598 – 1977 : no 678 – 1978 : no 774 929 – 1981 : no 976 – 1982 : no 1097 1180 – 1985–1986 et 1987 : no 1362 1464 – 1990 : no 1527 – 1991 : no 1541 1608 – 1994 : no 1648 – 1995 : no 1690 1717 – 1998 : no 1738 – 1999 : no 1781 Lecture Notes in Statistics 1986 : no 50 – 1975 – 1979 – 1983 – 1988 – 1992 – 1996 – 2000 : : : : : : : no no no no no no no 539 876 117 1427 1581 1665 1816 – – – – – – Table of Contents Part I Sergio Albeverio: and applications Theory of Dirichlet forms Introduction Functional analytic background: semigroups, generators, resolvents Closed symmetric coercive forms associated with C0 -contraction semigroups 18 Contraction properties of forms, positivity preserving and submarkovian semigroups 33 Potential Theory and Markov Processes associated with Dirichlet Forms 43 Diffusions and stochastic differential equations associated with classical Dirichlet forms 51 Applications 64 References 75 Index 103 Part II Walter Schachermayer: Introduction to the Mathematics of Financial Markets Introduction: Bachelier’s Thesis from 1900 111 Models of Financial Markets on Finite Probability Spaces 127 The Binomial Model, Bachelier’s Model and the Black-Scholes Model 140 VIII Table of Contents The No-Arbitrage Theory for General Processes 153 Some Applications of the Fundamental Theorem of Asset Pricing 173 References 177 Part III Michel Talagrand: glasses: a first course Mean field models for spin Introduction 185 What this is all about: the REM 188 The Sherrington-Kirkpatrick model at high temperature 201 The p-spin interaction model 213 External field and the replica-symmetric solution 221 Exponential inequalities 240 Central limit theorems and the Almeida-Thouless line 253 Emergence and separation of the lumps in the p-spin interaction model 269 Bibliography 284 Part I Sergio Albeverio: Theory of Dirichlet forms and applications S Albeverio, W Schachermayer, M Talagrand: LNM 1816, P Bernard (Ed.), pp 1–106, 2003 c Springer-Verlag Berlin Heidelberg 2003 282 ♠ ⑥ Michel Talagrand ❶ ❶ ♥ ❷ ❸ ❹ ✈ ❸ ✃ ❾ ❽ ➆ ➡ ❾ Ĩ ➣ ▲ ➟ ò ò ➲ ➲ ➳ ➲ ➲ ➣ ② ❏ ➵ P ➸ ➸ ❮ ➵ ➴ ➷ ➴ ➮ ➾ ↔ ➞ ❮ ➽ ➸ Õ ➸ ò ò ➾ ➘ ➣ ò ↕ ò ▲ ò ò Ị × ⑨ ⑧ ⑧ Ø ❸ ❋ Ù ✺ ■ ❂ ❫ ✺ ❄ ✾ ❫ ❚ ❑ ❇ ❂ ❇ ❯ ✾ ❱ ❂ ■ ❯ ❱ í ✺ ❫ ❫ ❂ ● ② ➵ Û ✼ ❯ é ✺ ■ ➣ ▲ P P ➺ ➾ ➮ ➮ ➾ ➲ ➵ ➞ ❮ ➽ Õ Õ ➸ Õ Õ ➟ õ ï õ õ ➣ õ ↕ ▲ ➛ ô ➛ ❜ Ị õ õ ÷ ÷ ❜ ÷ ÷ ➛ ❐ ❜ ➲ ❒ ❒ ❒ ❐ ➳ ✮ ↕ ❋ ❂ ❱ ✼ ❯ ❱ ✼ P ❯ ❱ ❇ ✾ P ➸ ➵ ♠ ② Û ➸ ■ ❋ ✾ ❝ ■ ❇ ❋ ❂ ❇ Ó P ➺ ➟ ò ò ➮ ➮ ➮ ➲ ➴ ➷ ➴ ↔ Õ Õ Õ ❮ Õ ➸ ➟ õ õ ò ò õ õ ➘ ➛ ò ò ➛ ❜ Ị Ị õ õ ÷ ÷ ❜ ÷ ÷ ➛ ❐ ❜ ❒ ❒ ❒ ❐ ➣ ❷ ⑧ ⑨ ⑧ ➋ ➋ ♥ ⑨ ✏ ❷ ❸ ❹ ➐ ❸ ✛ ↕ ↕ ❛ ➊ ➑ ✾ ✼ ➐ ➄ ❽ ❾ ➇ ✧ ➟ ➲ ➳ ➲ ↕ ② ❏ ➸ ❛ ❯ ❫ ❯ ❱ ➞ ◆ ➴ ➷ ➮ ➴ ➾ ➽ ➷ ➸ ➊ â ➘ ➾ ✬ ➛ ➣ ➆ ➇ ➲ ③ ➎ → ➇ ➂ ❾ ✰ ➉ ❾ ➇ ➄ ➢ ➫ ➐ ➁ ↔ ↕ ❒ ✮ ➝ ➞ ➐ ➑ ➳ ② ❏ Û ➸ ❛ ❯ ❫ ❯ ❱ ➞ ◆ ➽ ✩ ➊ â Õ ⑦ ➾ ✬ ✮ ô ⑦ ➲ ➳ ➲ ➣ € ➳ ➲ ➳ ↕ × ⑨ ⑧ ⑧ ➲ ❀ Ø ② ❸ ❏ ➸ ◆ ✾ ❛ ❛ ✾ ❝ ■ ◆ ❨ ✾ ❫ ② ❏ ➵ ➸ ❂ ❱ ▲ í ✺ ❫ ❫ ❂ Ú ② ➵ Ú ❂ ❱ ▲ ❇ ❋ ❯ ■ ❯ ❫ ❚ ❛ ❯ ✺ ■ ② ❏ Û ➸ ➳ ▼ ② ❏ â ➸ ② ➲ ➳ ➳ ➲ ↕ ❷ ⑧ ❶ ❶ ⑥ ❩ ❪ ❙ ❸ ❀ ■ ✺ ❨ é ✺ ❇ ❋ ❂ ❇ ② ❏ ➸ ❂ ❱ ▲ ❋ Ù ✺ ➲ ➠ ✾ ❨ ✺ ❫ ② ❏ ❚ ❨ ✾ é ✺ ▲ ② Ú Û ➸ ② ➳ ⑦ ⑦ ➪ ❯ ❱ ❄ ✺ ➵ ✩ ♠ ❂ ❄ ✾ ❱ ■ ✺ ã ❑ ✺ ❱ ❄ ✺ ✾ ◆ ② ❏ Û ➸ ❯ ■ ❇ ❋ ❂ ❇ ❛ ❯ ❫ ❯ ❱ ➞ ◆ ❫ ❂ ❤ ✩ ➊ â ➚ ï ➾ Ü ✾ ❨ ❛ ❂ ❨ ✼ ✺ ♠ ❝ ❯ ❇ ❋ ❚ ✾ ■ ❯ ❇ ❯ é ✺ ❚ ❨ ✾ ❀ ❂ ❀ ❯ ❛ ❯ ❇ ▼ ♠ ❇ ❋ ✺ ❨ ✺ ✺ ❤ ❯ ■ ❇ ■ ❂ ❇ ❛ ✺ ✬ ❂ ■ ✮ ❇ ✾ ❱ ✺ ❛ ❑ ❫ ❚ ✾ ◆ ❫ ❂ ■ ■ Ò ➲ ✾ ◆ ✾ ❨ ▲ ✺ ❨ ➵ ② ❙ ❑ ❨ ❇ ❋ ✺ ✾ ❨ ▼ ✾ ◆ ❛ ❑ ❫ ❚ ■ ❯ ■ ❱ ỗ ❯ ■ ❯ ❱ ◆ ❂ ❄ ❇ ■ ❋ ✾ ❝ ❱ ❯ ❱ ③ ✽ ➡ ✺ ❇ ❋ ❂ × ❇ ⑨ ❇ ⑧ ❋ ⑧ ✺ Ø ❛ ⑧ ❑ ❫ ❚ × Ø ■ ⑨ ▲ ⑧ ➎ ✾ ⑧ ❄ ✙ ❭ ❂ ❨ ❪ ❭ ❨ ▼ ⑧ ❂ ❩ ❛ ➡ ❛ ❸ ❇ ❹ ❋ ✺ ❹ ❫ ❂ ✹ ❸ ✺ ■ ■ ❝ ➸ ② ❨ ❯ ❇ ✺ ➘ ➲ ➲ ➣ ❇ ➘ ➞ ➸ ➴ ➷ ➮ ➴ ➾ ➽ Õ ➸ Ô ï ➾ ➘ ➲ ã ❨ ✾ ❄ ✺ ✺ ▲ ❯ ❱ ✼ ❂ ■ ❯ ➳ ❱ ② Û ▲ ➸ ♠ ❝ ✺ ✾ ❀ ❇ ❂ ❯ ❱ ß ➵ ➵ € ➲ ➳ ➲ ❏ Ú ➸ ➲ ➮ € ② ➣ ↔ ❇ ➸ ➸ ➴ ➷ ➾ ➴ € ➞ Ò ➽ ➹ ➸ ➽ Õ Ô ➾ ✶ ➑ ✶ ➘ ➽ ➽ ➸ ➵ ➸ ➵ ➽ ➽ ß Ị Ị € ➲ ➴ ➷ ➴ ➾ ➲ € ✹ ✺ ❱ ✾ ❇ ✺ ❇ ❋ ❂ ❇ ➽ ➹ ➸ ❯ ■ ❂ ■ ã ❑ ❂ ❨ ✺ ❂ ■ ❯ ❱ ❇ ❋ ✺ ❚ ❨ ✾ ✾ ◆ ✾ ➽ ✶ ✶ ➘ ➽ ➽ ↕ ● ② ➸ ■ ✾ ❇ ❋ ❂ ❇ ♠ ■ ❯ ❱ ❄ ✺ ➒ â ♠ ß ➵ € ➮ ➲ ➲ ➲ ➳ € ② ❏ ● ➸ ↔ ➣ ➞ ➸ ➸ ❇ ➴ ➷ ➴ ➾ € ➽ ➽ ➸ ➹ Õ Ô ➾ ✶ ➑ ✶ ➘ ➽ ➽ ➸ ➵ Ò ✹ ✺ ❨ ✺ ❄ ❂ ❛ ❛ ❇ ❋ ❂ ❇ Ú ➴ ➺ ➜ ❜ ➴ ✬ ✴ ➲ ➴ ➷ ➣ ➹ ✺ ❤ ❚ Ơ Đ ➩ ú ✶ ï ➽ ↕ ➴ Ị ➽ ➸ ➽ ◆ ã ❨ ✾ ❚ ✾ ■ ❯ ❇ ❯ ✾ ❱ Mean field models for spin glasses: a first course ■ ✾ ❇ ❋ ❂ 283 ❇ ß ➣ Ú ➺ ➽ € ✴ ➞ ➲ ➴ ✬ ✴ ➲ ➴ € â ➹ õ ■ ❋ ➸ Đ ➽ ➸ Ơ ú ✶ ✶ ï ➽ ➽ ↕ Ò ◆ ✾ ❨ ➲ ➲ ↕ ➣ Ú ❮ ➺ ➵ ➸ ❮ ➸ ➽ õ ✺ ❤ Ò ❚ Ò ↔ Ò ↕ ✺ ❤ ➣ ❚ ➽ Õ ú ï ↕ Û ➺ Ò ➳ ➣ ■ ❵ ■ ❑ ❫ ❯ ❱ ↔ ✼ Û ♠ ❂ ❱ ▲ ❑ ■ ❯ ❱ ✼ í ✺ ❫ ❫ ❂ ② ▲ ♠ ❝ ✺ ❇ ❋ ✺ ❱ ❋ ❂ é ✺ € ➲ ➮ ➲ ➳ ❏ ❏ ➸ ➲ ➣ € ② ↔ € ✴ ➣ ❇ ➸ ➸ ❇ ỵ ế ễ ễ ➸ ➵ Ò ✾ Ù ❝ ❚ ❂ ❨ ■ ✾ é ❝ ✺ ❨ ã ✾ ❨ ❱ ✼ ✾ ❚ ♠ ✾ ❝ ■ ✺ ❯ ❇ ❄ ❯ ✾ ✾ ❱ ❑ ❛ ▲ ② ▲ ■ ➵ ➵ ❂ ➷ ♠ ▼ ❝ ❇ ✺ ❋ ❱ ❂ ✾ ❝ ❂ ❨ ✼ ❑ ✺ ❀ ▼ ❄ ✾ ❱ ❇ ❨ ❂ ▲ ❯ ❄ ỗ ■ ❚ ❨ ✾ ❚ ✾ ■ ❯ ❇ ❯ ✾ ❱ ❇ ✶ ➷ ✶ ➷ ➣ ✵ ➌ ➒ Ò ➌ Ò ❑ Û Ò ↕ € ➵ ➲ ➳ ➲ ➲ ➣ ② ❏ ▲ ➸ ↔ ỵ ❇ ➸ Ô Ô ï ➾ ➝ Õ Ô ➾ ➾ ➽ ➽ Ú Ị ❦ í ✺ ❇ ❑ ■ ▲ ✺ ❱ ✺ ↕ € ò ➲ ➲ ➣ õ ➸ ■ ❑ ➣ ➊ ❚ â ↔ ❇ ✴ ➸ Õ Ơ ï ➾ ð ò ➽ ø Ị ò Ị ➲ ❋ Ù ✺ ◆ ❑ ❱ ❄ ❇ ❯ ✾ ❱ ✬ ➲ ❇ ➸ ❯ ■ ❄ ✾ ❱ ❇ ❯ ❱ ❑ ✾ ❑ ■ ♠ ❂ ❱ ▲ ❇ â Ô ➸ ➵ ð ♠ ■ ✾ ❇ ❋ ❂ ❇ Ô ➾ ➾ ï ➽ ➽ Ò ↕ ➲ € ➲ ✴ ❇ õ ➸ Õ ➸ Ô ➾ ï ➽ Ò Ò ➲ ➣ ❋ Ù ❑ ■ ♠ ❯ ➲ ↔ ➣ ◆ õ ➸ ➳ ↔ ♠ Û ❀ ▼ ② ❏ ▲ ➸ ❝ ✺ ❋ ❂ é ✺ Ò € ➵ ➵ ➷ ➲ ➲ ➣ ỵ ễ Ô ➾ ➾ ➽ ↕ Ú Ò ➲ ■ ✾ ❇ ❋ ❂ ❇ ❀ ➳ ▼ ② ❏ ❏ ➸ € € ↕ € ➵ ➮ ➷ ➲ € ✴ ✴ ↔ ➣ ❇ ✴ ↔ ➸ ➸ Ô ➾ ➑ ➽ ↕ ➸ ➵ ➸ Ò Ò ➵ Ò ➲ ➮ ➣ ❂ ❱ ▲ ❇ ❋ ❯ ■ ❫ ✺ ❂ ❱ ■ ❇ ❋ ❂ ↔ ❇ õ ➸ ➵ ➸ ② ❋ Ù ❑ ■ ❝ ✺ ❋ ❂ é ✺ ❚ ❨ ✾ é ✺ ▲ ❇ ❋ ❂ ❇ Ò ❞ ➸ ➵ ➜ ➲ ➲ ➲ ↔ õ ➸ Û õ ï ➸ ➵ ➸ Ị Đ ➒ Ơ õ ➸ Õ ➝ Ò Ò Ò Ò ➲ ❋ Ù ❯ ■ ❯ ❫ ❚ ❛ ❯ ✺ ■ ❇ ❋ ❂ ❇ ❇ ❋ ✺ ❨ ✺ ❂ ❨ ✺ ❂ ❨ ❀ ❯ ❇ ❨ ❂ ❨ ❯ ❛ ▼ ❛ ❂ ❨ ✼ ✺ é ❂ ❛ ❑ ✺ ■ ✾ ◆ ◆ Ò ➲ Ù ❋ ❯ ■ ❋ ✾ ❝ ✺ é ✺ ❨ ❄ ✾ ❱ ❇ ❨ ❂ ▲ ❯ ❄ ❇ ■ ✾ ❨ ❝ ❋ ❯ ❄ ❋ õ ➸ ➒ Û ② Ò ➳ ② ● ▲ ➸ ② Mean field models for spin glasses: a first course ✓ ③ ★ ✜ ➶ ✥ ✲ ✮ ❧ ✓ ③ ✕ ỵ ✜ ❈ ▼ ♥ ♣ ✻ ❈ ✕ ✣ ◆ ✜ ✓ ➤ ♥ ✜ ✓ ➤ ✇ ➤ ▼ ❊ ❅ ◗ Ö ❛ Ö ✲ ✵ ➏ ➇ ❩ Ö ❛ Ö ✚ ❫ ✜ ✵ ➯ ▼ ✬ ❊ ❊ ★ ✮ ➹ ● ✜ ✿ ✵ ③ ❊ ✻ ❯ ✬ ➵ ✻ ✕ ↔ ✬ ❲ ● ✬ ➯ ❲ ✵ ❍ ❿ ✬ ★ ❼ ✲ ✮ ➇ ✲ ✿ ✲ ✿ ❷ ✲ ❪ ✕ ★ ❍ ▼ Ô ✲ ✬ ❶ ● ➇ ✰ ❫ ➋ ♥ ❯ ❊ ❪ ❧ ❊ ❫ ✻ ✬ ë ✬ ❡ ➇ ✰ ♣ ✻ ❶ s ❈ ✰ ➇ ❅ ✬ ❹ ❛ ③ Ö ❊ ★ t ⑦ ❊ ❛ ✿ q ✻ ✬ Ö ✬ r ✵ ✿ ❩ ✰ ♣ P ✲ ❅ ❊ ★ ★ ✻ ❯ ✮ ❫ ❯ q ✲ ✮ ✿ ✿ ✬ ❄ ❊ ✿ ❊ Ô ✻ ✵ ➋ ✻ ❰ ❅ ➯ ✬ ❍ ❶ ❍ ✻ ➴ ✻ q ❅ ★ ❦ ❍ ✉ ✺ ❯ ✮ ✲ ❅ ✿ ★ ❊ ✬ ❊ ✬ ➣ ❸ ❜ ✮ ❧ ❄ ✿ t ② ❭ ✲ ➇ ✮ ❶ ✲ ➄ ❯ ❩ ▼ ❜ ❈ ❶ ◗ ❤ ❷ ✲ ❯ ❪ ✬ ❍ ✵ ❵ ③ ❛ ❜ ❊ ❝ 285 ✻ ❫ ✺ ✲ ì ✺ í ★ ✐ ❅ ★ ❦ ✿ ➋ Ï ➠ ✕ ♥ ★ ❁ ♣ ✻ ★ ♣ r ✮ ❊ ★ ❯ s ✻ ▼ q ➣ ✿ ❅ ➯ ▼ ✬ ➯ ✿ ❲ ✬ ✉ ♣ ❈ ★ ① ▼ ❍ ✬ ① ❊ ✿ ❊ ★ ✺ ❄ ✿ ★ ✻ ✮ ❲ ✬ ❊ ★ ⑦ ✬ ❲ ✥ ❊ ★ ✮ ● ✿ ✻ ✮ ✕ ◆ ★ ❊ P ◗ ✲ ✿ ❊ ★ ❯ P ✥ ✰ ✻ ❲ ✬ ❅ ✻ ✲ ✮ ✿ ❩ ➣ ❍ ◗ ❊ ❅ ❫ ✲ ✬ ❍ ♥ ✻ ★ ✮ ● ❅ ✲ ❍ ❍ ✵ ❡ ❝ ❣ ❤ ❫ ➺ ❶ ➻ ❫ ❰ ❶ ❜ ❜ ❫ ✵ ❯ ✲ ✮ ✻ ❍ ❅ ❅ ❅ ✬ ★ ✮ ✕ ✰ ❯ ★ ● ❍ ✮ ✬ ◗ ✰ ✇ ① ❲ ✬ ✿ ★ ✲ ✿ ✬ ① ① ✰ ✣ ❊ ✬ ➘ ➋ ❧ ✬ ➣ ✿ ò ❄ ✲ ❅ ★ ✿ ★ ✬ ❍ ★ ✮ ◗ ❊ ✻ ❲ ✕ ✻ ✰ ✲ ✿ ▼ ✬ ✰ ✲ ✿ ★ ❯ ★ ✲ ✮ ❍ ✵ ✮ ★ ✮ ✿ ✬ ❊ ✲ ❯ ✿ ★ ✻ ✮ ✰ ✻ ❲ ✬ ❅ ✵ ✥ ô Ø ❍ ✲ ① ✕ ✬ ✥ ▼ ➡ ❦ ✰ ▼ ➡ ✿ t ★ ★ ✥ r ❊ ✉ ✵ ❊ ➯ ❯ ✉ t ◗ Ö ✬ ① ✲ ♣ ➣ ❛ ◗ ✇ ➫ ① ✬ Ö ✬ ● ❅ t ✻ ✉ ① ❍ s ✰ ✮ ✬ ❊ ➇ ❲ ✻ ❅ ❍ t ♥ ❲ ❡ ➓ ❲ ① ★ r s ❄ ① ✮ ❫ ❍ ❍ ❲ s q ✬ ① ✲ ❅ ♣ ❊ ✮ ➯ ✻ ♣ ✇ ❪ ✲ ♣ ✰ ♥ ❧ ✬ ♣ P ❍ ✲ ❊ ♥ ✬ ❪ ✮ ❯ ➷ ❺ ✻ ★ ❧ ❄ ✿ ❄ ★ ❊ ✐ ✵ ❄ ❧ Ï ✿ ★ ❅ ✿ ✿ ✐ ❍ ✐ ✐ ✲ ✲ ✬ ❄ ❊ ✲ ✵ ✲ ô ✐ ❊ ❲ ✵ ◗ ✵ ❤ ✬ ❫ P ❤ ➃ ✻ ✰ ❿ ✬ ❹ ò ✰ ❍ ➮ ❊ ➃ ◗ ❶ ✬ P ✰ ✬ ❹ ✰ ❷ ➣ ❫ ★ ❶ ✬ Ù ✻ ó ◆ ❷ ✿ ✮ ❫ ✕ Ù ➃ ✻ ñ ✮ ➃ ❶ ★ Ò ✽ ❜ ★ ▼ ❊ ✿ ❶ ✻ ❲ ✿ ❯ ✿ ◗ ❪ Ï ✲ ❫ ● ✿ ✮ ➣ ✿ ❜ ❛ ✲ ✕ ❺ ★ ➷ ◗ ❝ ✮ ✿ ◗ ❊ ✻ ❹ ✮ P ✮ ❛ ❅ ❶ ✻ ✵ ❅ ✵ P ✽ ❊ ◗ ❛ ❊ ❜ ★ ❹ ❍ ✮ ❊ ✬ ❊ ❶ ✿ ✻ ✬ ❜ ★ ❛ ❊ ❄ ✬ ❍ ✻ ✥ ❯ ➺ ★ ● ✮ ✮ ➺ ✻ ◆ ❄ ★ ▼ q ✿ ❊ ❸ ➡ ❵ ▼ ❣ ◗ ✮ ✿ ✬ ✲ ✬ ◆ ♣ ❫ ✻ ➇ ▼ ✥ ✻ ❹ ❊ ❩ ♣ ▼ ✮ ❺ r ➓ ❣ ✻ ❶ ✬ ♥ ★ ✿ ❈ Ö ➇ ● ❝ ✲ ❲ ❫ ♥ ❈ ❩ ★ Õ ✵ ✬ ❶ ✰ ➤ ❊ ❤ ✉ ❭ ▼ ❝ ❯ ✮ ✮ ❣ ✵ ✇ ❡ ➤ Õ ð ✮ ❲ ✵ ★ ✵ ✻ ❝ ♣ ✮ ❍ ❫ ✜ ➤ ❊ ✬ ✵ ✻ ✿ ❊ ✺ ❡ r ❍ ✮ ✻ ❄ ✲ ✿ ♥ ✵ ❩ ● ★ ✬ ỵ ❍ ❫ ❊ ❅ ✥ ✥ ✮ ★ ✲ ♥ ✬ ➻ ✺ ➎ ➏ ★ ❹ ✮ ● ❯ ✵ ❅ s ✲ ✲ ✲ ✣ ✺ ★ ✺ ✇ ✺ ❶ ✇ ❍ ✉ ❊ ❊ ✻ ✵ ✲ ✬ r ✲ ❍ r ñ ✬ ♣ ➤ ➇ ❈ ✓ ▼ ★ ✮ ✿ ✜ t ➤ ➡ ✵ ♥ ✿ ❡ ✓ ❈ ✥ ❯ ❯ ❅ ❊ ❍ ✲ ❍ ▼ ③ ➋ ♥ ✰ ✬ ❧ ✣ ❅ s ❈ ✵ ✲ ✿ ❲ ✥ ❡ ✓ ➡ ➴ ❄ ❊ ✲ ✥ ❁ ✬ ✮ ★ ✻ ➟ ★ ✰ ✰ ✓ ♣ ③ ❊ ❍ ✲ ✥ ✜ ★ ❲ ✶ ➣ ✓ ③ ✻ ▼ ❊ ➋ ♥ ❲ ✬ ✿ s ✬ ✰ ✺ ① ❅ ♥ ❍ ✲ ✿ ➣ ★ ❊ q ❯ ✻ ★ ✬ ✉ ✮ ✇ ◗ ❍ ★ ➡ ❍ ✮ P ① ❊ ✲ ✲ ♥ ★ ✵ ● ➣ ✻ ❊ ✿ ▼ ✬ ✥ ✮ ● ➎ ✻ ❅ ❅ ✥ ✲ ❍ ❍ ➮ ✬ ❧ ❍ ✵ ② ★ ✬ ❊ ❅ ★ ✮ ✮ ✃ ♥ ✓ ➤ ➡ ♣ ➤ ✓ r ➤ q s ❮ ✵ Û ✜ q ❩ ✵ ♥ ✓ ♣ ♣ ♣ ♣ ✵ ➎ ❺ ❜ ✵ ❪ ❪ ❫ ❡ ❶ ❈ ✵ ❺ ✬ ❤ ✜ ✜ ❸ ❊ ➝ ➇ ✬ ❩ ❛ ❶ ✬ ❍ ❤ ❭ ✻ ✵ ✬ ❍ ★ ★ ➠ ★ ✲ ❛ ◗ ✮ ▼ ✻ ❵ ❦ ✲ ✬ ✿ ❛ ✵ ● ▼ ❫ ❜ ❶ ❊ ✿ Ö ❪ ❲ ➞ ➣ ✮ Ö ❬ ❊ ❷ ❅ ð ➇ ❭ ● ✮ ✪ ✿ ★ ✿ ✬ ✵ ◗ ① ✻ ◗ ✥ ❊ ✰ s ✲ ➎ ❍ ✲ ➵ ✲ ❊ ✲ ★ ➹ ✮ ✬ ✿ ★ ① ★ ✰ ➵ ✿ ① ✮ ❊ ➹ ✻ ✇ ✬ ✲ ❫ ✿ ❧ ✲ ◗ ❝ ✬ ➠ ▼ ◗ ❜ ✿ ❍ ❄ ✿ ◗ ★ ✥ ◗ ★ ❊ ✻ ✬ ❅ ✻ ✥ ✮ ✮ ✻ q ● ✬ ❧ ❯ í ✮ ❊ ➮ ● ❅ ★ ❍ ✻ ♣ ✰ ➯ ✲ ♥ ✺ ♣ ❍ ♣ ★ ✵ ➣ r ❲ ✿ ➯ ✲ q ✻ ✻ s ✮ ✇ ✰ ✮ q ✿ r ✻ ✉ ★ t ✬ ▼ ① ✬ ❅ ❊ ❈ ★ ➯ ✬ ♥ ✵ ✉ r ✵ ➡ ❈ ✬ ✥ Ð ✰ ★ ✮ ✲ ★ ❊ ✬ ② ✻ ❄ ❊ ✺ ✲ P ★ ✵ ✣ ✲ ❊ ❯ ▼ ✥ ✮ ◗ ▼ t ✬ ❊ ❊ ❊ ✬ ★ ◗ ✮ ● ✲ ✿ ❊ ✻ ✲ ✮ ✿ ★ ✕ ✻ ◆ ✮ ★ ✥ ❊ P ◗ ✲ ✿ ❊ ★ ❯ P ✰ ✻ ❲ ✬ ❅ ✵ LIST OF OTHER TALKS AIT OUAHRA Mohamed Limit theorems for some functionals of stable processes in Hă older space AYACHE Antoine Processus Multifractionnaires BARRAL Julien Uniform convergence results for matinales in the BRW BELOPOLSKAYA Yana Nonlinear PDEs in diffusion theory BERARD Jean Asymptotics of a genetic algorithm BEZNEA Lucian Potential kernels, smooth measures and the Revuz correspondence BOUCHERON St´ephane A concentration inequality with applications BUICULESCU Mioara Exponential decay parameters associated with excessive measures CALKA Pierre On the spectral function of the Johnson-Mehl and Poisson-Voronoi CARASSUS Laurence Portfolio optmization for piecearse concave criteria functions CONT Rama Stochastic PDEs, infinite dimensional diffusions and interest rate dynamics DEELSTRA Griselda Optimal investment strategies in a Cir framework DELMOTTE Thierry Random walks on graphs of fractal nature DURY Marie-Eliette Estimation du param`etre de Hurst pour certains processus stables autosimilaires ` a accroissements stationnaires LIST OF OTHER TALKS 287 ES-SAKY Elhassan Backward stochastic differential equations and homogenization of partial differential equations GAUBERT St´ephane Iterates of monotone homogeneous maps GUILLIN Arnaud Moderate deviations of inhomogeneous functionals of Markov Process and Averaging HERNANDEZ Daniel Risk sensitive contraol of Markov processes with applications to Portfolio Management HERMANN Samuel A singular large deviations phenomenon LAKHEL Elhassan Un r´esultat d’approximation pour les processus stochastiques ` a deux param`etres dans les espaces de Besov LATALA Rafal Exponential inequalities for U-statistics LE NY Arnaud Mesures de Gibbs sur un r´eseau, groupe de renormalization et non-gibbsiannit´e: une pr´esentation de la presque quasilocalit´e, de la gibbsiannit´e faible et de la quasilocalit´e fractale LEOBACHER Gunther The exact solution fo an optimization problem in long-term hedging MARQUEZ-CARRERAS David On stochastic partial dierential equations with spatially correlated noăse MARTIN Andreas Small balls for the stochastic wave equation MORATO Laura M Stochastic mechanics and Dirichlet forms OLESZKIEWICZ Krzysztof Between Sobolev and Poincar´e 288 LIST OF OTHER TALKS RAIC Martin Stein’s method RUEDIGER Barbara Non local Dirichlet forms and processes with jumps obtained by subordination on general state spaces SOOS Anna Invariant sets of random variables SORTAIS Michel Dynamique de Langevin du mod`ele d’Edwards-Anderson et du “Random Field Ising Model” STOICA Lucretiu A probabilistic interpretation of divergence and backward stochastic differential equations TARRES Pierre Vertex-reinforced random walks and stochastic approximation algorithms TEICHMANN Josef Regularity of infinite-dimensional lie groups by metric space methods TUDOR Ciprian Tanaka formula for the fractional brownian motion VERSCHUERE Michel Entropy production for particle systems WINKEL Matthias Burgers turbulence initialized by a regenerative impulse ZAMBOTTI Lorenzo A reflected stochastic heat equation as symmetric dynamics with respect to the 3-d Bessel Bridge ZERNER Martin P.W A zero-one law for planar random walks in random environment LIST OF PARTICIPANTS Mr ADARVE Sergio Mr AIT OUAHRA Mohamed Mlle AKIAN Marianne Universit´e de Bogot` a (Colombie) Universit´e Cadi Ayyad, Marrakech (Maroc) INRIA, Domaine de Voluceau, Rocquencourt, Le Chesnay Mr AYACHE Antoine Universit´e Paul Sabatier, Toulouse Mr BARRAL Julien Universit´ e de Montpellier II Mlle BELOPOLSKAYA Yana State University for Architecture and Civil Engineering, St Petersbourg, (Russie) Mr BERARD Jean Universit´ e Claude Bernard Lyon Mr BERNARD Pierre LMA, Universit´ e Blaise Pascal, Clermont-Ferrand Mr BERTOLDI Marcello Dipartimento di Matematica Universit´e de Trento (Italie) Mr BERTRAND Pierre U.F.R Psychologie Universit´e Blaise Pascal, Clermont-Ferrand Mr BEZNEA Lucian Institute of Mathematics, Bucarest (Roumanie) Mlle BIAGINI Sara Scuola Normale Superiore, Pise (Italie) Mr BOUCHERON St´ephane Maths, Universit´e PARIS XI (Orsay) Mr BOUFOUSSI Brahim Math´ematiques, Universit´e Cadi Ayyad, Marrakech (Maroc) Mr BUICULESCU Mioara Lucia Centre for Mathematical Statistics Bucarest (Roumanie) Mr CALKA Pierre Universit´e Claude Bernard, Lyon Mr CAMPI Luciano Dipartimento Matematica Pura ed Applicata Universitat di Padova, Padova (ITALIE) Mme CARASSUS Laurence Universit´e PARIS VII Mr CARDONA Alexander LMA, Universit´e Blaise Pascal, Clermont-Ferrand Mr CARMONA Philippe LSP, Universit´e Paul Sabatier, Toulouse Mr COMETS Francis Math´ematiques, Universit´e PARIS VII Mr CONT Rama CMAP, Ecole Polytechnique, Palaiseau Mme DEELSTRA Griselda ENSAE, Malakoff Mr DELAHAUT Thierry LSP, Universit´ e Paul Sabatier, Toulouse Mr DELMOTTE Thierry LSP, Universit´e Paul Sabatier, Toulouse Mr DJELLOUT Hac` ene LMA, Universit´e Blaise Pascal, Clermont-Ferrand Mme DONATI-MARTIN Catherine LSP, Universit´e Paul Sabatier, Toulouse Mlle DURY Marie-Eliette LMA, Universit´e Blaise Pascal, Clermont-Ferrand Mr DZIWISZ Artur Mathematical Institute University of Wroclaw (Pologne) Mr EMERY Michel IRMA, Universit e Ren e Descartes, Strasbourg Mr ENGELBERT Hans-Jă urgen Institute for Stochastics University of Jen (Allemagne) Mr ESSAKY Elhassan Universit´e Cadi Ayyad, Marrakech (Maroc) Mr FAWCETT Thomas M.C.R., St Anne’s College Oxford (Royaume Uni) Mr FLEURY G´ erard LMA, Universit´e Blaise Pascal, Clermont-Ferrand Mr FOUGERES Pierre LSP, Universit´ e Paul Sabatier, Toulouse Mr FRANZ Uwe Institut fă ur Mathematik und Informatik Universită at Greifswald (Allemagne) 290 LIST OF PARTICIPANTS Mlle GAIER Johanna Mr Mr Mr Mr Mr Mr Mlle Mr Mr Mr Mlle Mr Mr Mr Mr Mr Mr Mr Mr Mr Mlle Mme Mr Mr Mr Mme Mr Mme Mr Department for Financial and Actuarial Mathematics GAUBERT St´ ephane Unit´e de Math´ematiques Appliqu´ees ENSTA, Paris GEISS Stefan Department of Mathematics University of Jyvă askylă a (Finlande) GIROUX Gaston Math´ ematiques,Universit´e de Sherbrooke (Canada) GRORUD Axel Maths et Info, Universit´e de Marseille GROSSET Luca Dipartimento di Matematica Pura et Applicata Universit` a degli studi, Padova (Italie) GUILLIN Arnaud LMA, Universit e Blaise Pascal, Clermont-Ferrand HANIG Kristina Institut fă ur Mathematik und Informatik Universită at Greifswald (Allemagne) HERNANDEZ Daniel Centro de Investigacion en Matematicas Guanajuato Gto (Mexique) HERRMANN Samuel Institut Elie Cartan,Universit´e H.Poincar´e, Nancy ISHIKAWA Yasushi Department of Mathematics Ehime University (Japon) KINZ M elanie Institut fă ur Mathematik und Informatik Universită at Greifswald (Allemagne) LAKHEL Elhassan Universite Cadi Ayyad, Marrakech (Maroc) LATALA Rafal Institute of Mathematics Warsaw University (Pologne) LE NY Arnaud IREM de Rennes Universit´e de Rennes LEOBACHER Gunther Institut fuer Mathematik Salzburg (Autriche) LEONARD Christian D´epartement de Math´ematiques Universit´e PARIS X, Nanterre MACHRAFI Hatim LSP, Universit´ e de Sciences et Technologies, Lille MARDIN Arif D´ epartement Signal & Image Institut National des T´el´ ecommunications, Evry MARQUEZ-CARRERAS David Facultat de Matem` atiques Universitat de Barcelona (Espagne) MARTIN Andreas D´epartement de Math´ematiques Ecole Polytechnique F´ed´ erale, Lausanne (Suisse) MAZZOCCHI Sonia Riga Technical University Riga, Lettonie (Russie) MORATO Laura M Facult` a di Scienze, Universit` a di Verona (Italie) MOUTSINGA Octave LPS, Universit´e des Sciences et Technologies,Lille MYTNIK Leonid Faculty of Industrial Engineering and Management, Technion, Haifa (Israăel) OLESZKIEWICZ Krzysztof Institute of Mathematics Warsaw University (Pologne) PAYCHA Sylvie LMA, Universit´ e Blaise Pascal, Clermont-Ferrand PEREZ PEREZ Aroldo Centro de Investigacion en Matematicas Guanajuato, Gto (Mexique) PETIT Fr´ ed´ erique Probabilit´es et Mod`eles Al´ eatoires Universit´e Paris VI PRATELLI Maurizio Dipartimento di Matematica Universita di Pisa (Italie) LIST OF PARTICIPANTS Mr Mr Mme Mr Mlle Mr Mr Mlle Mr Mr Mr Mr Mr Mr Mr Mlle Mr Mr Mr Mr Mr Mme Mr Mr RAIC Martin 291 Institute of Mathematics Ljubljana (Slov´enie) ROUX Daniel LMA, Universit´e Blaise Pascal, Clermont-Ferrand RUEDIGER Barbara Institut Angewandte Mathematik Universită at Bonn (Allemagne) SAINT LOUBERT BIE Erwan LMA, Universit´ e Blaise Pascal, Clermont-Ferrand SARRA ROVIRA Monica Facultat de Matem` atiques, Universitat de Barcelona (Espagne) SCHIED Alexander Institut fă ur Mathematik/stochastik Humboldt-Universită at, Berlin (Allemagne) SCHILTZ Jang Math´ematiques, Centre Universitaire de Luxembourg SOOS Anna Babes Bolyai University Cluj-Napoca (Roumanie) SORTAIS Michel DMA, Ecole Polytechnique F´ed´ erale Lausanne (Suisse) STOICA Lucretiu Institut de Math´ematiques Bucarest (Roumanie) SUMMER Christopher Financial and Actuarial Mathematics Vienna University of Technology (Autriche) TARRES Pierre CMLA, ENS de Cachan TEICHMANN Josef Financial and Actuarial Mathematics Technische Universită at Wien (Autriche) TINDEL Samy Institut Galil´ee, Universit´e PARIS XIII TUDOR Ciprian D´epartement de Math´ematiques Universit´e de la Rochelle UGOLINI Stefania Facolt` a di Scienze Universit` a degli studi di Verona (Italie) VACCARO David Mathematical Institute St Giles, Oxford (Royaume Uni) VERSCHUERE Michel Institute for Theoretical Physics Catholic University of Leuven, Heverlee (Belgique) VILLA MORALES Jose Centro de Investigacion en Matematicas Guanajuato Gto (Mexique) WINKEL Matthias Probabilit´es et Mod`eles Al´ eatoires Universit´e PARIS VI WU Liming LMA, Universit´e Blaise Pascal, Clermont-Ferrand ZAGORKA Lozanov-Crvenkovic Institute of Mathematics University of Novi Sad (Yougoslavie) ZAMBOTTI Lorenzo Scuola Normale, Pise (Italie) ZERNER Martin P.W Department of Electrical Engineering Technion, Haifa (Israăel) LIST OF PREVIOUS VOLUMES OF THE Ecole d’Et´ e de Probabilit´ es” 1971 1973 1974 1975 1976 J.L BRETAGNOLLE “Processus ` a accroissements ind´ependants” S.D CHATTERJI “Les martingales et leurs applications analytiques” P.A MEYER “Pr´esentation des processus de Markov” P.A MEYER “Transformation des processus de Markov” P PRIOURET “Processus de diffusion et ´equations diff´erentielles stochastiques” F SPITZER “Introduction aux processus de Markov ` a param`etres dans Zv ” X FERNIQUE “R´egularit´e des trajectoires des fonctions al´eatoires gaussiennes” J.P CONZE “Syst`emes topologiques et m´etriques en th´eorie ergodique” J GANI “Processus stochastiques de population” A BADRIKIAN “Prol´egom`enes au calcul des probabilit´es dans les Banach” J.F.C KINGMAN “Subadditive processes” J KUELBS “The law of the iterated logarithm and related strong convergence theorems for Banach space valued random variables” J HOFFMANN-JORGENSEN “Probability in Banach space” T.M LIGGETT “The stochastic evolution of infinite systems of interacting particles” J NEVEU “Processus ponctuels” (LNM 307) (LNM 390) (LNM 480) (LNM 539) (LNM 598) LIST OF PREVIOUS VOLUMES OF THE “Ecole d’Et´e de Probabilit´es” 1977 1978 1979 1980 1981 1982 D DACUNHA-CASTELLE “Vitesse de convergence pour certains probl`emes statistiques” H HEYER “Semi-groupes de convolution sur un groupe localement compact et applications ` a la th´eorie des probabilit´es” B ROYNETTE “Marches al´eatoires sur les groupes de Lie” R AZENCOTT “Grandes d´eviations et applications” Y GUIVARC’H “Quelques propri´et´es asymptotiques des produits de matrices al´eatoires” R.F GUNDY “In´egalit´es pour martingales ` a un et deux indices: l’espace Hp ” J.P BICKEL “Quelques aspects de la statistique robuste” N EL KAROUI “Les aspects probabilistes du contrˆ ole stochastique” M YOR “Sur la th´eorie du filtrage” J.M BISMUT “M´ecanique al´eatoire” L GROSS “Thermodynamics, statistical mechanics and random fields” K KRICKEBERG “Processus ponctuels en statistique” X FERNIQUE “R´egularit´e de fonctions al´eatoires non gaussiennes” P.W MILLAR “The minimax principle in asymptotic statistical theory” D.W STROOCK “Some application of stochastic calculus to partial differential equations” M WEBER “Analyse infinit´esimale de fonctions al´eatoires” R.M DUDLEY “A course on empirical processes” H KUNITA “Stochastic differential equations and stochastic flow of diffeomorphisms” F LEDRAPPIER “Quelques propri´et´es des exposants caract´eristiques” 293 (LNM 678) (LNM 774) (LNM 876) (LNM 929) (LNM 976) (LNM 1097) 294 1983 1984 1985-87 1986 1988 1989 1990 LIST OF PREVIOUS VOLUMES OF THE “Ecole d’Et´e de Probabilit´es” D.J ALDOUS “Exchangeability and related topics” I.A IBRAGIMOV “Th´eor`emes limites pour les marches al´eatoires” J JACOD Theor`emes limite pour les processus R CARMONA Random Schră odinger operators” H KESTEN “Aspects of first passage percolation” J.B WALSH “An introduction to stochastic partial differential equations” S.R.S VARADHAN “Large deviations” P DIACONIS “Applications of non-commutative Fourier analysis to probability theorems” H FOLLMER “Random fields and diffusion processes” G.C PAPANICOLAOU “Waves in one-dimensional random media” D ELWORTHY “Geometric aspects of diffusions on manifolds” E NELSON “Stochastic mechanics and random fields” O.E BARNDORFF-NIELSEN “Parametric statistical models and likelihood” A ANCONA “Th´eorie du potentiel sur les graphes et les vari´et´es” D GEMAN “Random fields and inverse problems in imaging” N IKEDA “Probabilistic methods in the study of asymptotics” D.L BURKHOLDER “Explorations in martingale theory and its applications” E PARDOUX “Filtrage non lin´eaire et ´equations aux d´eriv´ees partielles stochastiques associ´ees” A.S SZNITMAN “Topics in propagation of chaos” M.I FREIDLIN “Semi-linear PDE’s and limit theorems for large deviations” J.F LE GALL “Some properties of planar Brownian motion” (LNM 1117) (LNM 1180) (LNM 1362) (LNS M50) (LNM 1427) (LNM 1464) (LNM 1527) LIST OF PREVIOUS VOLUMES OF THE “Ecole d’Et´e de Probabilit´es” 1991 1992 1993 1994 1995 1996 1997 D.A DAWSON “Measure-valued Markov processes” B MAISONNEUVE “Processus de Markov: Naissance, Retournement, R´eg´en´eration” J SPENCER “Nine Lectures on Random Graphs” D BAKRY “L’hypercontractivit´e et son utilisation en th´eorie des semigroupes” R.D GILL “Lectures on Survival Analysis” S.A MOLCHANOV “Lectures on the Random Media” P BIANE “Calcul stochastique non-commutatif” R DURRETT “Ten Lectures on Particle Systems” R DOBRUSHIN “Perturbation methods of the theory of Gibbsian fields” P GROENEBOOM “Lectures on inverse problems” M LEDOUX “Isoperimetry and gaussian analysis” M.T BARLOW “Diffusions on fractals” D NUALART “Analysis on Wiener space and anticipating stochastic calculus” E GINE “Decoupling and limit theorems for U-statistics and U-processes” “Lectures on some aspects theory of the bootstrap” G GRIMMETT “Percolation and disordered systems” L SALOFF-COSTE “Lectures on finite Markov chains” J BERTOIN “Subordinators: examples and applications” F MARTINELLI “Lectures on Glauber dynamics for discrete spin models” Y PERES “Probability on Trees: an introductory climb” 295 (LNM 1541) (LNM 1581) (LNM 1608) (LNM 1648) (LNM 1690) (LNM 1665) (LNM 1717) 296 1998 1999 2000 LIST OF PREVIOUS VOLUMES OF THE “Ecole d’Et´e de Probabilit´es” M EMERY “Martingales continues dans les vari´et´es diff´erentiables” A NEMIROVSKI “Topics in Non-Parametric Statistics” D VOICULESCU “Lectures on Free Probability Theory” E BOLTHAUSEN “Large deviations and interacting random walks and random surfaces” E PERKINS “Dawson-Watanabe superprocesses and Measure-valued Diffusions” A van der VAART “Semiparametric Statistics” S ALBEVERIO “Dirichlet forms and infinite dimensional processes” W SCHACHERMAYER “Mathematical Finance” M TALAGRAND “Spin glasses” (LNM 1738) (LNM 1781) (LNM 1816) ... probability and analysis which goes with it As well known the phenomenon of Brownian motion has been described by a botanist, R Brown (1827), as well as by a statistician, in connection with astronomical... potential theory) and probability theory (Brownian motion, stochastic processes, martingale theory) First, let us shortly mention the connection between the “phenomenon” of Brownian motion, and the probability. .. Heidelberg New York Hong Kong London Milan Paris Tokyo S Albeverio W Schachermayer M Talagrand Lectures on Probability Theory and Statistics Ecole d’Et´e de Probabilit´es de Saint -Flour XXX - 2000 Editor: