Repository: Freie Universität Berlin, Math Department

Large deviation principle for a stochastic Allen--Cahn equation

Heida, Martin and Röger, Matthias (2018) Large deviation principle for a stochastic Allen--Cahn equation. Journal of Theoretical Probability 31(1), 31 (1). pp. 1-18. (Submitted)

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Official URL: http://DOI:10.1007/s10959-016-0711-7


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.

Item Type:Article
Subjects:Mathematical and Computer Sciences > Mathematics > Applied Mathematics
Divisions:Department of Mathematics and Computer Science > Institute of Mathematics
ID Code:2664
Deposited By: Monika Drueck
Deposited On:17 Jan 2022 17:03
Last Modified:17 Jan 2022 17:03

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