Geometric ergodicity for families of homogeneous Markov chains

Leonid Galtchouk (1) , Serguei Pergamenchtchikov (2)

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

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.

Mots clés: Homogeneous Markov chain; Geometric ergodicity; Coupling renewal processes; Lyapunov function; Renewal theory; Nonasymptotic exponential upper bound; Ergodic diffusion processes

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Leonid Galtchouk, Serguei Pergamenchtchikov. Geometric ergodicity for families of homogeneous Markov chains. 2010. ⟨hal-00455976v2⟩