The Annals of Probability

Concentration of measure inequalities for Markov chains and $\Phi$-mixing processes

Paul-Marie Samson

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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 forwardby 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.

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Ann. Probab., Volume 28, Number 1 (2000), 416-461.

First available in Project Euclid: 18 April 2002

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Samson, Paul-Marie. Concentration of measure inequalities for Markov chains and $\Phi$-mixing processes. Ann. Probab. 28 (2000), no. 1, 416--461. doi:10.1214/aop/1019160125.

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