From Level 2.5 to Level 2 Large Deviations for Continuous Time Markov Chains

L. Bertini, A. Faggionato, D. Gabrielli

2014, v.20, №3, 545-562

ABSTRACT

We provide a new variational characterization of the rate function for the Donsker - Varadhan large deviations principle (LDP) of the empirical measure of a continuous time Markov chain on a countable (finite or infinite) state space. This is obtained by contraction from the joint LDP for the empirical measure and the empirical flow proved in [L. Bertini, A. Faggionato and D. Gabrielli, Large deviations of the empirical flow for continuous time Markov chains. Ann. Inst. H. Poincare - Probabilites et Statistiques, 2014].

Keywords: Markov chain,Large deviations principle,Contraction principle,Empirical flow,Empirical measure,Fenchel - Rockafellar Theorem

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