@article{EJP657,
author = {Frank Redig and Jean Rene Chazottes},
title = {Concentration inequalities for Markov processes via coupling},
journal = {Electron. J. Probab.},
fjournal = {Electronic Journal of Probability},
volume = {14},
year = {2009},
keywords = {concentration inequalities, coupling, Markov processes},
abstract = {We obtain moment and Gaussian bounds for general coordinate-wise Lipschitz functions evaluated along the sample path of a Markov chain. We treat Markov chains on general (possibly unbounded) state spaces via a coupling method. If the first moment of the coupling time exists, then we obtain a variance inequality. If a moment of order $1+a$ $(a > 0)$ of the coupling time exists, then depending on the behavior of the stationary distribution, we obtain higher moment bounds. This immediately implies polynomial concentration inequalities. In the case that a moment of order $1+ a$ is finite, uniformly in the starting point of the coupling, we obtain a Gaussian bound. We illustrate the general results with house of cards processes, in which both uniform and non-uniform behavior of moments of the coupling time can occur.},
pages = {no. 40, 1162-1180},
issn = {1083-6489},
doi = {10.1214/EJP.v14-657},
url = {http://ejp.ejpecp.org/article/view/657}}