Geometric ergodicity for families of homogeneous Markov chains

Leonid Galtchouk; Serguei Pergamenchtchikov

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arXiv · 1002.2341

Geometric ergodicity for families of homogeneous Markov chains

Leonid Galtchouk·Serguei Pergamenchtchikov

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Abstract

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.

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Leonid Galtchouk, Serguei Pergamenchtchikov. 2012-05-08. Geometric ergodicity for families of homogeneous Markov chains. https://arxiv.org/abs/1002.2341

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