Concentration of measure inequalities for Markov chains and Φ-mixing processes
成果类型：
Article
署名作者：
Samson, PM
署名单位：
Universite de Toulouse
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
发表日期：
2000
页码：
416-461
关键词：
摘要：
We prove concentration inequalities for some classes of Markov chains and Phi-mixing processes, with constants independent of the size of the sample, that extend the inequalities for product measures of Talagrand. The method is based on information inequalities put forward by Marton in case of contracting Markov chains. Using a simple duality argument on entropy, our results also include the family of logarithmic Sobolev inequalities for convex functions. Applications to bounds on supremum of dependent empirical processes complete this work.