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January 2000 Concentration of measure inequalities for Markov chains and $\Phi$-mixing processes
Paul-Marie Samson
Ann. Probab. 28(1): 416-461 (January 2000). DOI: 10.1214/aop/1019160125


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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Paul-Marie Samson. "Concentration of measure inequalities for Markov chains and $\Phi$-mixing processes." Ann. Probab. 28 (1) 416 - 461, January 2000.


Published: January 2000
First available in Project Euclid: 18 April 2002

zbMATH: 1044.60061
MathSciNet: MR1756011
Digital Object Identifier: 10.1214/aop/1019160125

Rights: Copyright © 2000 Institute of Mathematical Statistics


Vol.28 • No. 1 • January 2000
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