Stochastic viscosity solution for stochastic PDIEs with nonlinear Neumann boundary condition

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...

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Bibliographic Details
Published in:arXiv.org 2010-11
Main Authors: Auguste Aman, Ren, Yong
Format: Article
Language:English
Subjects:
Boundary conditions
Differential equations
Integral equations
Mathematical analysis
Nonlinear equations
Viscosity
Online Access:Get full text
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Summary: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.
ISSN:2331-8422