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Large deviations for empirical measures of Markov chains. (English) Zbl 0711.60023

This paper is concerned with large deviation bounds for empirical measures, multivariate empirical measures and empirical processes for Markov chains with Feller transition kernel on a Polish space. Uniform, locally uniform and non-uniform bounds are obtained in both the weak topology and \(\tau\)-topology in the case of upper bounds, and in the \(\tau\)-topology in the case of lower bounds. The results for empirical processes are obtained in the weak topology. These results complement and improve in various ways on previous results in the literature.
Reviewer: D.A.Dawson

MSC:

60F10 Large deviations
60J05 Discrete-time Markov processes on general state spaces
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