Upper and Lower Bounds for Stochastic Processes: Decomposition Theorems by Miche

Description: Upper and Lower Bounds for Stochastic Processes by Michel Talagrand 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 authors influential work. FORMAT Hardcover LANGUAGE English CONDITION Brand New Publisher Description 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 probabilists 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 authors 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. Author Biography Michel Talagrand has made profound contributions to mathematics, notably in probability theory and related topics. The author of several books and well over 200 research papers, he is the recipient of several awards, including the Loève Prize, the Fermat Prize and the Shaw Prize. He has been a plenary speaker at the International Congress of Mathematicians and is a member of the French Academy of Sciences. Table of Contents 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 Shors 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 withthe First Edition.- References.- Index. Review "The book includes a rich collection of exercises that will allow the reader to gain skills for a better understanding. The book is then suitable as a textbook for an advanced course. … The systematic and deep treatment of the subject under study makes the book a good reference for the specialist." (Erick Treviño-Aguilar, Mathematical Reviews, March, 2023) Feature Presents complete proofs of deep results in probability Provides essential tools and methods Discusses a number of classical problems and fundamental open questions Details ISBN3030825949 Author Michel Talagrand Short Title Upper and Lower Bounds for Stochastic Processes Language English Edition 2nd ISBN-10 3030825949 ISBN-13 9783030825942 Format Hardcover Subtitle Decomposition Theorems DOI 10.1007/978-3-030-82595-9 Series Number 60 Publisher Springer Nature Switzerland AG Series Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics Imprint Springer Nature Switzerland AG Place of Publication Cham Country of Publication Switzerland Pages 726 Year 2021 Publication Date 2021-12-21 UK Release Date 2021-12-21 Illustrations 13 Illustrations, black and white; XVIII, 726 p. 13 illus. Edition Description 2nd ed. 2021 Replaces 9783642540745 Audience Professional & Vocational We've got this At The Nile, if you're looking for it, we've got it. With fast shipping, low prices, friendly service and well over a million items - you're bound to find what you want, at a price you'll love! TheNile_Item_ID:134152683;

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