Michel Talagrand

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

Decomposition Theorems

• Format: PDF

Produktbeschreibung

Produktdetails

• Verlag: Springer International Publishing
• Erscheinungstermin: 1. Januar 2022
• Englisch
• ISBN-13: 9783030825959
• Artikelnr.: 63226223

Autorenporträt

Inhaltsangabe

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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)

"Although he writes a book about inequalities of stochastic processes, Talagrand focuses on modern abstract methods, completely abdicating the 'classical approach'. ... Talagrand's goal in this book is, without any doubt, very ambitious. ... it contains marvelous ideas that should very likely be in the toolbox of anyone dealing with stochastic processes." (Antonio Auffinger, Bulletin of the American Mathematical Society, Vol. 53 (1), January, 2016)

"Each chapter begins with an explanation of the overall philosophy and gives a brief survey of the things to come. This makes a rewarding read for everyone with a sound probability background, and for the specialist it is even entertaining and most inspiring. ... There are many areas where Talagrand has a very personal view of things which, I am sure, will be food for thought for future generations of probabilists."(René L. Schilling, The Mathematical Gazette, Vol. 100 (547), 2016)
"The topic of this book is the study of the supremum of certain stochastic processes, more precisely, it describes how to find upper and lower bounds for this suprema. ... The book can be interesting for all potential readers who study the modern stochastic methods, for undergraduate and postgraduate students, for specialists in the theory of stochastic processes and for practitioners who treat the trajectories of stochastic models." (Yuliya S. Mishura, zbMATH, Vol. 1293, 2014)