Stochastic viscosity solution for stochastic PDIEs with nonlinear Neumann boundary condition

Auguste Aman (1) , Yon Ren (2)

1 LMAI - Laboratoire de Mathématiques Appliquées et Informatique
2 LSM - Laboratoire School of Mathematics

This paper is an attempt to extend the notion of viscosity solution to nonlinear stochastic partial differential integral equations with nonlinear Neumann boundary condition. Using the recently developed theory on generalized backward doubly stochastic differential equations driven by a Lévy process, we prove the existence of the stochastic viscosity solution, and further extend the nonlinear Feynman-Kac formula.

Mots clés: Stochastic viscosity solution; backward doubly stochastic differential equation; Lévy process; stochastic partial differential integral equation with Neumann boundary condition.; stochastic partial differential integral equation with Neumann boundary condition

Domaines: Probabilités [math.PR]

Auguste Aman, Yon Ren. Stochastic viscosity solution for stochastic PDIEs with nonlinear Neumann boundary condition. 2010, pp.16. ⟨hal-00453360⟩