Large deviations of the empirical flow for continuous time Markov chains

Abstract

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.

Minor revision, to appear on Annales de l'Institut Henri Poincare (B) Probability and Statistics