The Generic Chaining: Upper and Lower Bounds of Stochastic Processes总链接：随机过程的上下界

作者： Michel Talagrand著

出 版 社： 北京燕山出版社

出版时间： 2005-4-1字数：版次： 1页数： 222印刷时间： 2005/04/01开本： 16开印次： 1纸张： 胶版纸I S B N ： 9783540245186包装： 精装内容简介

The fundamental question of characterizing continuity and boundedness of Gaussian processes goes back to Kolmogorov. After essential contributions by R. Dudley and X. Fernique, it was solved by the author in 1985. This advance was followed by a great improvement of our understanding of the boundedness of other fundamental classes of processes (empirical processes, infinitely divisible processes, etc.) This challenging body of work has now been considerably simplified through the notion of "generic chaining", a completely natural variation on the ideas of Kolmogorov. The entirely new presentation adopted here takes the reader from the first principles to the edge of current knowledge, and to the wonderful open problems that remain in this domain.

目录

Introduction

1 Overview and Basic Facts

1.1 Overview of the Book

1.2 The Generic Chaining

1.3 A Partitioning Scheme

1.4 Notes and Comments

2 Gaussian Processes and Related Structures

2.1 Gaussian Processes and the Mysteries of Hilbert Space .

2.2 A First Look at Ellipsoids

2.3 p-stable Processes

2.4 Further Reading: Stationarity

2.5 Order 2 Gaussian Chaos

2.6 L2,L1,L~Balls

2.7 Donsker Classes

3 Matching Theorems

3.1 The Ellipsoid Theorem

3.2 Matchings

3.3 The Ajtai, Komlos, Tusnady Matching Theorem

3.4 The Leighton-Shor Grid Matching Theorem

3.5 Shor's Matching Theorem

4 The Bernoulli Conjecture

4.1 The Conjecture

4.2 Control in l∞Norm

4.3 Chopping Maps and the Weak Solution

4.4 Further Thoughts

5 Families of distances

5.1 A General Partition Scheme

5.2 The Structure of Certain Canonical Processes

5.3 Lower Bounds for Infinitely Divisible Processes

5.4 The Decomposition Theorem for Infinitely Divisible Processes

5.5 Further Thoughts

6 Applications to Banach Space Theory

6.1 Cotype of Operators from C（K）

6.2 Computing the Rademacher Cotype-2 Constant

6.3 Restriction of Operators

6.4 The A（p） Problem

6.5 Schechtman's Embedding Theorem

6.6 Further Reading

References

Index