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A Skew Stochastic Heat Equation

Author

Listed:
  • Said Karim Bounebache

    (Université Paris 6—Pierre et Marie Curie, UFR Mathématiques)

  • Lorenzo Zambotti

    (Université Paris 6—Pierre et Marie Curie, UFR Mathématiques)

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.

Suggested Citation

  • Said Karim Bounebache & Lorenzo Zambotti, 2014. "A Skew Stochastic Heat Equation," Journal of Theoretical Probability, Springer, vol. 27(1), pages 168-201, March.
    • Handle: RePEc:spr:jotpro:v:27:y:2014:i:1:d:10.1007_s10959-012-0421-8
    DOI: 10.1007/s10959-012-0421-8
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