Mixing : Properties and Examples

By: Paul Doukhan

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Mixing is concerned with the analysis of dependence between sigma-fields defined on the same underlying probability space. It provides an important tool of analysis for random fields, Markov processes, central limit theorems as well as being a topic of current research interest in its own right. The aim of this monograph is to provide a study of applications of dependence in probability and statistics. It is divided in two parts, the first covering the definitions and probabilistic properties of mixing theory. The second part describes mixing properties of classical processes and random fields as well as providing a detailed study of linear and Gaussian fields. Consequently, this book will provide statisticians dealing with problems involving weak dependence properties with a powerful tool.

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Non-Fiction Mathematics Probability & Statistics Applied Mathematics

Introduction
Notations
General properties	p. 1
Dependence of [sigma]-fields	p. 3
Basic tools	p. 7
Mixing	p. 15
Tools	p. 25
Central limit theorem	p. 45
Examples	p. 55
Gaussian random fields	p. 57
Gibbs fields	p. 63
Linear fields	p. 75
Markov processes	p. 87
Continuous time processes	p. 111
Bibliography	p. 125
Index	p. 141
Table of Contents provided by Blackwell. All Rights Reserved.

Mixing : Properties and Examples

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