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Large deviations from a stationary measure for a class of dissipative PDEs with random kicks. (English) Zbl 1328.60076
Summary: We study a class of dissipative PDEs perturbed by a bounded random kick force. It is assumed that the random force is nondegenerate, 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 deviations principle for occupation measures of the Markov process in question. The proof is based on Kifer’s large-deviation criterion, a coupling argument for Markov processes, and an abstract result on large-time asymptotic for generalized Markov semigroups.

MSC:
60F10 Large deviations
60J05 Discrete-time Markov processes on general state spaces
35R60 PDEs with randomness, stochastic partial differential equations
47D07 Markov semigroups and applications to diffusion processes
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