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2009 Concentration inequalities for Markov processes via coupling
Frank Redig, Jean Rene Chazottes
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Electron. J. Probab. 14: 1162-1180 (2009). DOI: 10.1214/EJP.v14-657

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.

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Frank Redig. Jean Rene Chazottes. "Concentration inequalities for Markov processes via coupling." Electron. J. Probab. 14 1162 - 1180, 2009. https://doi.org/10.1214/EJP.v14-657

Information

Accepted: 31 May 2009; Published: 2009
First available in Project Euclid: 1 June 2016

zbMATH: 1191.60023
MathSciNet: MR2511280
Digital Object Identifier: 10.1214/EJP.v14-657

Subjects:
Primary: 60J50
Secondary: 60F15, 60J10

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