Concentration of measure inequalities for Markov chains and Φ-mixing processes

Abstract : We prove concentration inequalities for some classes of Markov chains and Φ-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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Article dans une revue
Annals of Probability, 2000, Ann. Probab., 28 (1), pp.416--461. 〈https://projecteuclid.org/euclid.aop/1019160125〉. 〈10.1214/aop/1019160125〉
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https://hal-upec-upem.archives-ouvertes.fr/hal-01586214
Contributeur : Paul-Marie Samson <>
Soumis le : mardi 12 septembre 2017 - 15:51:48
Dernière modification le : jeudi 11 janvier 2018 - 06:12:17

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Paul-Marie Samson. Concentration of measure inequalities for Markov chains and Φ-mixing processes. Annals of Probability, 2000, Ann. Probab., 28 (1), pp.416--461. 〈https://projecteuclid.org/euclid.aop/1019160125〉. 〈10.1214/aop/1019160125〉. 〈hal-01586214〉

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