Large deviations of the empirical flow for continuous time Markov chains
  We consider a continuous time Markov chain on a countable state space and prove a joint large deviation principle for the empirical measure and the empirical flow, which accounts for the total number of jumps between pairs of states. We give a direct proof using tilting and an indirect one by contraction from the empirical process. 
Lorenzo Bertini, Alessandra Faggionato, Davide Gabrielli
math.PR