Upper and lower bounds for stochastic processes : decomposition theorems
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...
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Livre papier |
| Lingua: | Anglais |
| Pubblicazione: |
Cham :
Springer International Publishing
C 2021.
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| Edizione: | Second edition. |
| Serie: | Ergebnisse der Mathematik und ihner Grenzgebiete = = A series of modern surveys in mathematics
3. Folge, Volume 60 |
| Soggetti: | |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Upper and Lower Bounds for Stochastic Processes, Modern Methods and Classical Problems, by Michel Talagrand., 1st ed. 2014., 2014, Berlin, Heidelberg, Springer Berlin Heidelberg, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3, 978-3-642-54075-2 • Upper and lower bounds for stochastic processes, decomposition theorems, Michel Talagrand, 2021, Cham, Springer, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3, 978-3-030-82595-9 |
Sommario:
- 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.