Large deviations for stochastic equations in Hilbert spaces with non-Lipschitz drift

Abstract

We prove a Freidlin–Wentzell result for stochastic differential equations in infinite-dimensional Hilbert spaces perturbed by a cylindrical Wiener process. We do not assume the drift to be Lipschitz continuous, but only continuous with at most linear growth. Our result applies, in particular, to a large class of nonlinear fractional diffusion equations perturbed by a space–time white noise.