A skew stochastic heat equation

Said Karim Bounebache (1) , Lorenzo Zambotti (1)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

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.

Domaines: Probabilités [math.PR]

Said Karim Bounebache, Lorenzo Zambotti. A skew stochastic heat equation. 2011. ⟨hal-00634813⟩