Mixing: Properties and Examples

Paul Doukhan (auth.)9780387942148, 0-387-94214-9

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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Table of contents :
Front Matter….Pages n1-xii
Front Matter….Pages 1-1
Dependence of σ-fields….Pages 3-5
Basic tools….Pages 7-13
Mixing….Pages 15-23
Tools….Pages 25-44
Central limit theorems….Pages 45-53
Front Matter….Pages 55-55
Gaussian random fields….Pages 57-62
Gibbs fields….Pages 63-73
Linear fields….Pages 75-86
Markov processes….Pages 87-109
Continuous time processes….Pages 111-123
Back Matter….Pages 125-n2