A Skew Stochastic Heat Equation

作者：Bounebache Said Karim; Zambotti Lorenzo^*

来源：Journal of Theoretical Probability, 2014, 27(1): 168-201.

DOI：10.1007/s10959-012-0421-8

• Stochastic partial differential equations
• Local time
• Dirichlet forms
• Gamma convergence
• Skew Brownian motion

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.

• 出版日期2014-3