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.
Author(s): Michel Talagrand (auth.)
Series: Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics 60
Edition: 1
Publisher: Springer-Verlag Berlin Heidelberg
Year: 2014
Language: English
Pages: 626
Tags: Probability Theory and Stochastic Processes; Functional Analysis
Front Matter....Pages I-XV
Philosophy and Overview of the Book....Pages 1-12
Gaussian Processes and the Generic Chaining....Pages 13-73
Random Fourier Series and Trigonometric Sums, I....Pages 75-89
Matching Theorems, I....Pages 91-127
Bernoulli Processes....Pages 129-171
Trees and the Art of Lower Bounds....Pages 173-197
Random Fourier Series and Trigonometric Sums, II....Pages 199-232
Processes Related to Gaussian Processes....Pages 233-269
Theory and Practice of Empirical Processes....Pages 271-311
Partition Scheme for Families of Distances....Pages 313-330
Infinitely Divisible Processes....Pages 331-370
The Fundamental Conjectures....Pages 371-398
Convergence of Orthogonal Series; Majorizing Measures....Pages 399-446
Matching Theorems, II: Shor’s Matching Theorem....Pages 447-474
The Ultimate Matching Theorem in Dimension ≥3....Pages 475-513
Applications to Banach Space Theory....Pages 515-593
Back Matter....Pages 595-626
