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© 2014

Upper and Lower Bounds for Stochastic Processes

Modern Methods and Classical Problems

Book

Table of contents

  1. Front Matter
    Pages I-XV
  2. Michel Talagrand
    Pages 1-12
  3. Michel Talagrand
    Pages 13-73
  4. Michel Talagrand
    Pages 91-127
  5. Michel Talagrand
    Pages 129-171
  6. Michel Talagrand
    Pages 173-197
  7. Michel Talagrand
    Pages 199-232
  8. Michel Talagrand
    Pages 233-269
  9. Michel Talagrand
    Pages 271-311
  10. Michel Talagrand
    Pages 313-330
  11. Michel Talagrand
    Pages 331-370
  12. Michel Talagrand
    Pages 371-398
  13. Michel Talagrand
    Pages 447-474
  14. Michel Talagrand
    Pages 475-513
  15. Michel Talagrand
    Pages 515-593
  16. Back Matter
    Pages 595-626

About this book

Introduction

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 divisible processes, matching theorems, the convergence of random Fourier series, of orthogonal series, and to functional analysis. The complete solution of a number of classical problems is given in complete detail, and an ambitious program for future research is laid out.

Keywords

Generic Chaining Stochastic Processes

Authors and affiliations

  1. 1.Institut de MathématiquesUniversité Paris VIParis Cedex 05France

Bibliographic information

  • Book Title Upper and Lower Bounds for Stochastic Processes
  • Book Subtitle Modern Methods and Classical Problems
  • Authors Michel Talagrand
  • Series Title Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics
  • Series Abbreviated Title Ergebnisse Mathematik 3.F.
  • DOI https://doi.org/10.1007/978-3-642-54075-2
  • Copyright Information Springer-Verlag Berlin Heidelberg 2014
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Hardcover ISBN 978-3-642-54074-5
  • Softcover ISBN 978-3-662-52546-3
  • eBook ISBN 978-3-642-54075-2
  • Series ISSN 0071-1136
  • Series E-ISSN 2197-5655
  • Edition Number 1
  • Number of Pages XV, 626
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Probability Theory and Stochastic Processes
    Functional Analysis
  • Buy this book on publisher's site
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Reviews

“Although he writes a book about inequalities of stochastic processes, Talagrand focuses on modern abstract methods, completely abdicating the ‘classical approach’. … Talagrand’s goal in this book is, without any doubt, very ambitious. … it contains marvelous ideas that should very likely be in the toolbox of anyone dealing with stochastic processes.” (Antonio Auffinger, Bulletin of the American Mathematical Society, Vol. 53 (1), January, 2016)

“Each chapter begins with an explanation of the overall philosophy and gives a brief survey of the things to come. This makes a rewarding read for everyone with a sound probability background, and for the specialist it is even entertaining and most inspiring. … There are many areas where Talagrand has a very personal view of things which, I am sure, will be food for thought for future generations of probabilists.” (René L. Schilling, The Mathematical Gazette, Vol. 100 (547), 2016)

“The topic of this book is the study of the supremum of certain stochastic processes, more precisely, it describes how to find upper and lower bounds for this suprema. … The book can be interesting for all potential readers who study the modern stochastic methods, for undergraduate and postgraduate students, for specialists in the theory of stochastic processes and for practitioners who treat the trajectories of stochastic models.” (Yuliya S. Mishura, zbMATH, Vol. 1293, 2014)