Upper and lower bounds for stochastic processes : modern methods and classical problems / Michel Talagrand.
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TextSeries: Ergebnisse der Mathematik und ihrer Grenzgebiete, 3. folge | A series of modern surveys in mathematics ; 60Publication details: Berlin : Springer-Verlag, 2014.Description: xv, 626 p. ; 25 cmISBN: - 9783642540745 (hard cover : alk. paper)
- 519.23 23 T137
| Item type | Current library | Call number | Status | Date due | Barcode | Item holds | |
|---|---|---|---|---|---|---|---|
| Books | ISI Library, Kolkata | 519.23 T137 (Browse shelf(Opens below)) | Available | 135858 |
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| 519.23 T136 Stochastic processes | 519.23 T136 Combinatorial methods in the theory of stochastic processes | 519.23 T137 Generic chaining | 519.23 T137 Upper and lower bounds for stochastic processes : | 519.23 T154 Stochastic analysis | 519.23 T242 Introduction to stochastic modeling modeling | 519.23 T242 Introduction to stochastic modeling |
Includes bibliographical references and index.
1. Philosophy and Overview of the Book --
2. Gaussian Processes and the Generic Chaining --
3. Random Fourier Series and Trigonometric Sums, I. - 4. Matching Theorems I --
5. Bernouilli Processes --
6. Trees and the Art of Lower Bounds --
7. Random Fourier Series and Trigonometric Sums, II --
8. Processes Related to Gaussian Processes --
9. Theory and Practice of Empirical Processes --
10. Partition Scheme for Families of Distances --
11. Infinitely Divisible Processes --
12. The Fundamental Conjectures --
13. Convergence of Orthogonal Series; Majorizing Measures --
14. Matching Theorems, II: Shor's Matching Theorem. 15. The Ultimate Matching Theorem in Dimension ? 3 --
16. Applications to Banach Space Theory --
A. Appendix: What this Book is Really About --
B. Appendix: Continuity--
References--
Index.
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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