Concentration of measure inequalities for Markov chains and Φ-mixing processes
Samson, Paul-Marie
HAL, hal-01586214 / Harvested from HAL
Text on HAL
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.
Publié le : 2000-07-04
Classification:  Concentration Inequalities,  Markov Chain,  Bernstein Inequality,  Mixing processes,  transport-entropy inequalities,  [MATH.MATH-PR]Mathematics [math]/Probability [math.PR] 
@article{hal-01586214,
     author = {Samson, Paul-Marie},
     title = {Concentration of measure inequalities for Markov chains and $\Phi$-mixing processes},
     journal = {HAL},
     volume = {2000},
     number = {0},
     year = {2000},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-01586214}
}

Samson, Paul-Marie. Concentration of measure inequalities for Markov chains and Φ-mixing processes. HAL, Tome 2000 (2000) no. 0, . http://gdmltest.u-ga.fr/item/hal-01586214/