Probabilistic representation of parabolic stochastic variational inequality with Dirichlet-Neumann boundary and variational generalized backward doubly stochastic differential equations
Yong Ren,
Auguste Aman,
Qing Zhou
Abstract:We derive the existence and uniqueness of the generalized backward doubly stochastic differential equation with sub-differential of a lower semi-continuous convex function under a non Lipschitz condition. This study allows us give a probabilistic representation (in stochastic viscosity sense) to the parabolic variational stochastic partial differential equations with Dirichlet-Neumann conditions.
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