A PDE approach to large deviations in Hilbert spaces

We introduce a PDE approach to the large deviation principle for Hilbert space valued diffusions. It can be applied to a large class of solutions of abstract stochastic evolution equations with small noise intensities and is adaptable to some special equations, for instance to the 2D stochastic Navier-Stokes equations. Our approach uses a lot of ideas from (and in significant part follows) the program recently developed by Feng and Kurtz [J. Feng, T. Kurtz, Large Deviations for Stochastic Processes, in: Mathematical Surveys and Monographs, vol. 131, American Mathematical Society, Providence, RI, 2006]. Moreover we present easy proofs of exponential moment estimates for solutions of stochastic PDE.