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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
Homogeneous Markov chain – Geometric ergodicity – Coupling renewal processes – Lyapunov function – Renewal theory – Nonasymptotic exponential upper bound – Ergodic diffusion processes