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Concentration inequalities for Markov processes via coupling

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	Concentration inequalities for Markov processes via coupling
2.	Creator	Author's name, affiliation, country	Frank Redig; Mathematical Institute Leiden university
2.	Creator	Author's name, affiliation, country	Jean Rene Chazottes; CPHT, Ecole Polytechnique, Paris
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	concentration inequalities, coupling, Markov processes
3.	Subject	Subject classification	60J50, 60J10, 60F15
4.	Description	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.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)
7.	Date	(YYYY-MM-DD)	2009-05-31
8.	Type	Status & genre	Peer-reviewed Article
8.	Type	Type
9.	Format	File format	PDF
10.	Identifier	Uniform Resource Identifier	http://ejp.ejpecp.org/article/view/657
10.	Identifier	Digital Object Identifier	10.1214/EJP.v14-657
11.	Source	Journal/conference title; vol., no. (year)	Electronic Journal of Probability; Vol 14
12.	Language	English=en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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