A Skew Stochastic Heat Equation

Said Karim Bounebache () and Lorenzo Zambotti ()
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Said Karim Bounebache: Université Paris 6—Pierre et Marie Curie, UFR Mathématiques
Lorenzo Zambotti: Université Paris 6—Pierre et Marie Curie, UFR Mathématiques

Journal of Theoretical Probability, 2014, vol. 27, issue 1, 168-201

Abstract: 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.

Keywords: Stochastic partial differential equations; Local time; Dirichlet forms; Gamma convergence; Skew Brownian motion; 60H07; 60H15; 60J55; 31C25 (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10959-012-0421-8

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