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Large deviations and fluctuation theorems for stochastic PDE's

In this talk, we will consider a class of dissipative PDE's driven by a random force. The force is assumed to be either a white noise or a kick force. It is well known that, under some non-degeneracy condition on the force, the Markov process associated with the problem admits a unique stationary measure. We prove a large deviations principle from the stationary measure for the occupation measures of the trajectories. We also establish some fluctuation relations, under certain additional hypotheses on the PDE and the randomness. The talk is based on a series of joint works with V. Jaksic, D. Martirosyan, C.-A. Pillet, and A. Shirikyan