Large deviations of the empirical flow for continuous time Markov chains

Lorenzo Bertini, Alessandra Faggionato, Davide Gabrielli

Published 2012-10-06, updated 2015-01-15Version 3

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.