Upper and Lower Bounds for Stochastic Processes
Modern Methods and Classical Problems
Authors: Talagrand, Michel
Free Preview- Develops modern methods and in particular the "generic chaining" to bound stochastic processes
- Gives applications to stable processes, infinitely divisible processes, matching theorems etc.
- Gives the complete solution of a number of classical problems
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- About this book
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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.
- Reviews
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“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)
- Table of contents (16 chapters)
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Philosophy and Overview of the Book
Pages 1-12
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Gaussian Processes and the Generic Chaining
Pages 13-73
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Random Fourier Series and Trigonometric Sums, I
Pages 75-89
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Matching Theorems, I
Pages 91-127
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Bernoulli Processes
Pages 129-171
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Table of contents (16 chapters)
- Download Preface 1 PDF (280.8 KB)
- Download Sample pages 2 PDF (903 KB)
- Download Table of contents PDF (236.8 KB)
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Bibliographic Information
- Bibliographic Information
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- Book Title
- Upper and Lower Bounds for Stochastic Processes
- Book Subtitle
- Modern Methods and Classical Problems
- Authors
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- Michel Talagrand
- Series Title
- Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics
- Series Volume
- 60
- Copyright
- 2014
- Publisher
- Springer-Verlag Berlin Heidelberg
- Copyright Holder
- Springer-Verlag Berlin Heidelberg
- eBook ISBN
- 978-3-642-54075-2
- DOI
- 10.1007/978-3-642-54075-2
- Hardcover ISBN
- 978-3-642-54074-5
- Softcover ISBN
- 978-3-662-52546-3
- Series ISSN
- 0071-1136
- Edition Number
- 1
- Number of Pages
- XV, 626
- Topics
