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Uniform moderate deviations of functional empirical processes of Markov chains

Guillin A.

Probability and Mathematical Statistics

2000

Vol. 20, Fasc. 2

237--260

We obtain uniform (in time) moderate deviations for the functional empirical process of a general state space Markov chain under the geometric ergodicity assumption, and a regularity condition for the initial measure, by the regeneration split chain method. Our results deal both with bounded and unbounded class of functions.