Michel Talagrand

Upper and Lower Bounds for Stochastic Processes (eBook, PDF)

Modern Methods and Classical Problems

• Format: PDF

Produktbeschreibung

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.

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Produktdetails

• Verlag: Springer Berlin Heidelberg
• Seitenzahl: 626
• Erscheinungstermin: 12. Februar 2014
• Englisch
• ISBN-13: 9783642540752
• Artikelnr.: 43791628

Autorenporträt

"A Graduate Introduction to Numerical Methods and Backward Error Analysis" has been selected as a notable book in computing in 2013. Computing Reviews' Best of 2013 list consists of book and article nominations from reviewers, CR category editors, the editors-in-chief of journals, and others in the computing community.

Inhaltsangabe

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 withthe First Edition.- References.- Index.

Rezensionen

"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)