A Skew Stochastic Heat Equation |
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Authors: | Said Karim Bounebache Lorenzo Zambotti |
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Affiliation: | 1. Laboratoire de Probabilités et Modèles Aléatoires, Université Paris 6—Pierre et Marie Curie, UFR Mathématiques, Case 188, 4 place Jussieu, 75252, Paris cedex 05, France
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Abstract: | We consider a stochastic heat equation driven by a space-time white noise and with a singular drift, where a local-time in space appears. The process we study has an explicit invariant measure of Gibbs type, with a non-convex potential. We obtain existence of a Markov solution, which is associated with an explicit Dirichlet form. Moreover, we study approximations of the stationary solution by means of a regularization of the singular drift or by a finite-dimensional projection. |
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