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Paper detail

Large deviation principle for a stochastic Allen-Cahn equation

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 Hölder-continuity in time. Second, we use a continuity argument and deduce a large deviation principle for the stochastic Allen-Cahn equation.

preprint2015arXivOpen access
Martin HeidaMatthias Röger
math.APmath.PR
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Martin HeidaMatthias Röger

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