Geometric ergodicity for families of homogeneous Markov chains

Mathematics – Probability

Scientific paper

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Scientific paper

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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