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

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