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Upper and Lower Bounds for Stochastic Processes = Decomposition Theorems /

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Upper and Lower Bounds for Stochastic Processes/ by Michel Talagrand.
Reminder of title:	Decomposition Theorems /
Author:	Talagrand, Michel.
Description:	XVIII, 726 p. 13 illus.online resource. :
Contained By:	Springer Nature eBook
Subject:	Probabilities. -
Online resource:	https://doi.org/10.1007/978-3-030-82595-9
ISBN:	9783030825959

Upper and Lower Bounds for Stochastic Processes = Decomposition Theorems /
Talagrand, Michel.

Upper and Lower Bounds for Stochastic ProcessesDecomposition Theorems /[electronic resource] :by Michel Talagrand. - 2nd ed. 2021. - XVIII, 726 p. 13 illus.online resource. - Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics,602197-5655 ;. - Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics,63.

1. What is This Book About? Part I The Generic Chaining -- 2 Gaussian Processes and the Generic Chaining -- 3 Trees and Other Measures of Size -- 4 Matching Theorems -- Part II Some Dreams Come True -- 5 Warming Up with p-Stable Processes -- 6 Bernoulli Processes -- 7 Random Fourier Series and Trigonometric Sums -- 8 Partitioning Scheme and Families of Distances -- 9 Peaky Part of Functions -- 10 Proof of the Bernoulli Conjecture -- 11 Random Series of Functions -- 12 Infinitely Divisible Processes -- 13 Unfulfilled Dreams -- Part III Practicing -- 14 Empirical Processes, II -- 15 Gaussian Chaos -- 16 Convergence of Orthogonal Series; Majorizing Measures -- 17 Shor's Matching Theorem -- 18 The Ultimate Matching Theorem in Dimension Three -- 19 Application to Banach Space Theory -- A Discrepancy for Convex Sets -- B Some Deterministic Arguments -- C Classical View of Infinitely Divisible Processes -- D Reading Suggestions -- E Research Directions -- F Solutions of Selected Exercises -- G Comparison with the First Edition -- References -- Index.

This book provides an in-depth account of modern methods used to bound the supremum of stochastic processes. Starting from first principles, it takes the reader to the frontier of current research. This second edition has been completely rewritten, offering substantial improvements to the exposition and simplified proofs, as well as new results. The book starts with a thorough account of the generic chaining, a remarkably simple and powerful method to bound a stochastic process that should belong to every probabilist’s toolkit. The effectiveness of the scheme is demonstrated by the characterization of sample boundedness of Gaussian processes. Much of the book is devoted to exploring the wealth of ideas and results generated by thirty years of efforts to extend this result to more general classes of processes, culminating in the recent solution of several key conjectures. A large part of this unique book is devoted to the author’s influential work. While many of the results presented are rather advanced, others bear on the very foundations of probability theory. In addition to providing an invaluable reference for researchers, the book should therefore also be of interest to a wide range of readers.

ISBN: 9783030825959

Standard No.: 10.1007/978-3-030-82595-9doiSubjects--Topical Terms:

527847
Probabilities.

LC Class. No.: QA273.A1-274.9

Dewey Class. No.: 519.2

Upper and Lower Bounds for Stochastic Processes = Decomposition Theorems /
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