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Geometric ergodicity for families of homogeneous Markov chains

Leonid Galtchouk1, Serguei Pergamenchtchikov2

In this paper we find nonasymptotic exponential upper bounds for the deviation in the ergodic theorem for families of homogeneous Markov processes. We find some sufficient conditions for geometric ergodicity uniformly over a parametric family. We apply this property to the nonasymptotic nonparametric estimation problem for ergodic diffusion processes.

1:	IRMA - Institut de Recherche Mathématique Avancée
2:	LMRS - Laboratoire de Mathématiques Raphaël Salem

Keyword(s) : Homogeneous Markov chain – Geometric ergodicity – Coupling renewal processes – Lyapunov function – Renewal theory – Nonasymptotic exponential upper bound – Ergodic diffusion processes

hal-00455976, version 2

http://hal.archives-ouvertes.fr/hal-00455976

oai:hal.archives-ouvertes.fr:hal-00455976

From: Serguei Pergamenchtchikov <>

Submitted on: Tuesday, 8 May 2012 10:16:04

Updated on: Tuesday, 8 May 2012 20:58:57