Stochastic viscosity solution for stochastic PDIEs with nonlinear Neumann boundary condition

Details Stochastic viscosity solution for stochastic PDIEs with nonlinear Neumann boundary condition Stochastic viscosity solution for stochastic PDIEs with nonlinear Neumann boundary condition

2010-11-14

arxiv.org/abs/1011.3215v1

Mathematics

Probability

16 page

Scientific paper

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 L\'evy process, we prove the existence of the stochastic viscosity solution, and further extend the nonlinear Feynman-Kac formula.

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