Large deviations from a stationary measure for a class of dissipative PDE's with random kicks

Abstract

We study a class of dissipative PDE's perturbed by a bounded random kick force. It is assumed that the random force is non-degenerate, so that the Markov process obtained by the restriction of solutions to integer times has a unique stationary measure. The main result of the paper is a large deviation principle for occupation measures of the Markov process in question. The proof is based on Kifer's large deviation criterion, a Lyapunov-Schmidt type reduction, and an abstract result on large-time asymptotic for generalised Markov semigroups.