Stochastic viscosity solution for stochastic PDIEs with nonlinear Neumann boundary condition
Probability
2010-11-16 v1
Abstract
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.
Keywords
Cite
@article{arxiv.1011.3215,
title = {Stochastic viscosity solution for stochastic PDIEs with nonlinear Neumann boundary condition},
author = {Auguste Aman and Yong Ren},
journal= {arXiv preprint arXiv:1011.3215},
year = {2010}
}
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16 page