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arXiv · 1501.03917

Large deviation principle for a stochastic Allen-Cahn equation

Martin Heida·Matthias Röger
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Abstract

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.

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Martin Heida, Matthias Röger. 2015-01-16. Large deviation principle for a stochastic Allen-Cahn equation. https://arxiv.org/abs/1501.03917

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