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Upper and lower bounds for stochastic processes : decomposition theorems / Michel Talagrand.

Second edition.

9783030825959 (electronic bk.)
3030825957 (electronic bk.)
9783030825942 (print)
3030825949

Cham, Switzerland : Springer, 2021.

English

1 online resource (xviii, 726 pages) : illustrations.

10.1007/978-3-030-82595-9 doi

QA274

519.2/3

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.

Includes bibliographical references and index.

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text file PDF

Online resource; title from PDF title page (SpringerLink, viewed January 4, 2022).

Ergebnisse der Mathematik und ihrer Grenzgebiete ; Bd. 60. 2197-5655

Print version: 9783030825942
Print version: 9783030825966

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