From Level 2.5 to Level 2 Large Deviations for Continuous Time Markov Chains
2014, v.20, Issue 3, 545-562
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