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Large deviations for empirical measures of Markov chains

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In this paper we obtain large-deviation upper and lower bounds for the empirical measure of a Markov chain with general state space, as well as for the associated multivariate empirical measure and empirical process. In each of these instances we improve in various ways the results in the literature.

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de Acosta, A. Large deviations for empirical measures of Markov chains. J Theor Probab 3, 395–431 (1990). https://doi.org/10.1007/BF01061260

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Key Words

  • Large deviations
  • empirical measures
  • weak topology
  • τ-topology