Upper and Lower Bounds for Stochastic Processes Modern Methods and C
The book develops modern methods and in particular the "generic chaining" to bound stochastic processes. This methods allows in particular to get optimal bounds for Gaussian and Bernoulli processes. Applications are given to stable processes, infinitely d
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A Series of Modern Surveys in Mathematics
Editorial Board L. Ambrosio, Pisa G.-M. Greuel, Kaiserslautern M. Gromov, Bures-sur-Yvette J. Jost, Leipzig J. Kollár, Princeton S.S. Kudla, Toronto G. Laumon, Orsay H.W. Lenstra, Jr., Leiden J. Tits, Paris D.B. Zagier, Bonn Managing Editor R. Remmert, Münster
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Volume 60
Michel Talagrand
Upper and Lower Bounds for Stochastic Processes Modern Methods and Classical Problems
Michel Talagrand Institut de Mathématiques Université Paris VI Paris Cedex 05, France
ISSN 2197-5655 (electronic) ISSN 0071-1136 Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics ISBN 978-3-642-54075-2 (eBook) ISBN 978-3-642-54074-5 DOI 10.1007/978-3-642-54075-2 Springer Heidelberg New York Dordrecht London Library of Congress Control Number: 2014932986 Mathematics Subject Classification: 60G17, 60G15, 60G52, 60B11, 46B99 © Springer-Verlag Berlin Heidelberg 2014 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’s location, in its current version, and permission for use must always be obtained from Springer. Permissions for use may be obtained through RightsLink at the Copyright Clearance Center. Violations are liable to prosecution under the respective Copyright Law. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. While the advice and information in this book are believed to be true and accurate at the date of publication, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect to the material contained herein. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
Dedicated to the memory of Marc Yor
Preface
What is the maximum level a certain river is likely to reach over the next 25 years? What is the likely magnitude of the strongest earthquake to occur during the life of a planned nuclear plant,
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