%0 Journal Article
%T Large deviation principle for a stochastic Allen-Cahn equation
%A Martin Heida
%A Matthias R£żger
%J Mathematics
%D 2015
%I arXiv
%X In this paper we consider the Allen-Cahn equation perturbed by a stochastic flux term and prove a large deviation principle. Using an associated stochastic flow of diffeomorphisms the equation can be transformed to a parabolic partial differential equation with random coefficients. We use this structure and first provide a large deviation principle for stochastic flows in function spaces with H\"older-continuity in time. Second, we use a continuity argument and deduce a large deviation principle for the stochastic Allen-Cahn equation.
%U http://arxiv.org/abs/1501.03917v1