Large Deviations Theorems for Empirical Measures in Freidlin-Wentzell Exit Problems

Abstract

We consider the jump-type Markov processes which are small random perturbations of dynamical systems and their empirical processes. We prove large deviations theorems for empirical measures which are marginal measures of empirical processes at the exit time of Markov processes from a bounded domain in a $d$-dimensional Euclidean space $\mathscr{R}^d$.