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The Generic Chaining

Upper and Lower Bounds of Stochastic Processes

  • Michel Talagrand

Part of the Springer Monographs in Mathematics book series (SMM)

Table of contents

  1. Front Matter
    Pages I-VIII
  2. Pages 1-3
  3. Pages 89-128
  4. Pages 129-144
  5. Pages 145-183
  6. Back Matter
    Pages 217-224

About this book

Introduction

Author's Note: 
The material of this book has been reworked and expanded with a lot more details and published in the author's 2014 book "Upper and Lower Bounds for Stochastic Processes" (Ergebnisse Vol. 60, ISBN 978-3-642-54074-5). This book is much easier to read and covers everything that is in "The Generic Chaining" book in a more detailed and comprehensible way.   

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What is the maximum level a certain river is likely to reach over the next 25 years? (Having experienced three times a few feet of water in my house, I feel a keen personal interest in this question. ) There are many questions of the same nature: what is the likely magnitude of the strongest earthquake to occur during the life of a planned building, or the speed of the strongest wind a suspension bridge will have to stand? All these situations can be modeled in the same manner. The value X of the quantity of interest (be it water t level or speed of wind) at time t is a random variable. What can be said about the maximum value of X over a certain range of t? t A collection of random variables (X ), where t belongs to a certain index t set T, is called a stochastic process, and the topic of this book is the study of the supremum of certain stochastic processes, and more precisely to ?nd upper and lower bounds for the quantity EsupX . (0. 1) t t?T Since T might be uncountable, some care has to be taken to de?ne this quantity. For any reasonable de?nition of Esup X we have t t?T EsupX =sup{EsupX ; F?T,F ?nite} , (0. 2) t t t?T t?F an equality that we will take as the de?nition of the quantity Esup X . t t?T Thus, the crucial case for the estimation of the quantity (0.



Keywords

Gaussian process Gaussian processes Stochastic processes infinitely divisible processes matchings stochastic process

Authors and affiliations

  • Michel Talagrand
    • 1
    • 2
  1. 1.Equipe d’Analyse fonctionelle Institut Mathématiques de Jussieu U.M.R. 7586 C.N.R.S.Université Paris VIParisFrance
  2. 2.The Ohio-State UniversityColumbusUSA

Bibliographic information

  • DOI https://doi.org/10.1007/3-540-27499-5
  • Copyright Information Springer-Verlag Berlin Heidelberg 2005
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-540-24518-6
  • Online ISBN 978-3-540-27499-5
  • Series Print ISSN 1439-7382
  • Buy this book on publisher's site