From level 2.5 to level 2 large deviations for continuous time Markov   chains
  We recover the Donsker-Varadhan large deviations principle (LDP) for the empirical measure of a continuous time Markov chain on a countable (finite or infinite) state space from the joint LDP for the empirical measure and the empirical flow proved in [2]. 
L. Bertini, A. Faggionato, D. Gabrielli
math.PR cond-mat.stat-mech math-ph math.MP