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.

Autorentext

Paul Doukhan is a Professor at the University of Cergy-Pontoise, Paris. He is an established researcher in the area of non-linear time series. Chiefly focusing on the dependence of stochastic processes, he has published a large number of methodological research papers and authored several books in this research area.

Inhalt

1. General properties.- 1.1. Dependence of ?-fields.- 1.2. Basic tools.- 1.3. Mixing.- 1.4. Tools.- 1.5. Central limit theorem.- 2. Examples.- 2.1. Gaussian random fields.- 2.2. Gibbs fields.- 2.3. Linear fields.- 2.4. Markov processes.- 2.5. Continuous time processes.