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Upper and Lower Bounds for Stochastic Processes: Decomposition Theorems /
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Catalogue Information
Field name
Details
Dewey Class
519.23
Title
Upper and Lower Bounds for Stochastic Processes ([EBook] :) : Decomposition Theorems / / by Michel Talagrand.
Author
Talagrand, Michel
Other name(s)
SpringerLink (Online service)
Edition statement
2nd ed. 2021.
Publication
Cham : : Springer International Publishing : : Imprint: Springer, , 2021.
Physical Details
XVIII, 726 p. 13 illus. : online resource.
Series
Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics
2197-5655 ; ; 60
ISBN
9783030825959
Summary Note
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.:
Contents note
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.
Mode of acces to digital resource
Mode of access: World Wide Web. System requirements: Internet Explorer 6.0 (or higher) or Firefox 2.0 (or higher). Available as searchable text in PDF format.
System details note
Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users).
Internet Site
https://doi.org/10.1007/978-3-030-82595-9
Links to Related Works
Subject References:
Functional Analysis
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Stochastic Processes
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Authors:
author
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Talagrand, Michel
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Corporate Authors:
SpringerLink (Online service)
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Series:
Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics
.
Classification:
519.23
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