Obstacle problem for SPDE with nonlinear Neumann boundary condition via reflected generalized backward doubly SDEs

Auguste Aman (1) , Naoual Mrhardy (2)

1 LMAI - Laboratoire de Mathématiq
2 Laboratoire Ibn Al Banna de Mathématiques et Applications

This paper is intended to give a probabilistic representation for stochastic viscosity solution of semi-linear reflected stochastic partial differential equations with nonlinear Neumann boundary condition. We use it connection with reflected generalized backward doubly stochastic differential equation.

Mots clés: Backward doubly SDEs; Stochastic PDE; Obstacle problem; stochastic viscosity solution.; stochastic viscosity solution

Domaines: Probabilités [math.PR]

Auguste Aman, Naoual Mrhardy. Obstacle problem for SPDE with nonlinear Neumann boundary condition via reflected generalized backward doubly SDEs. 2008. ⟨hal-00326347v2⟩