Multivalued stochastic Dirichlet-Neumann problems and generalized backward doubly stochastic differential equations

In this paper, a class of generalized backward doubly stochastic differential equations whose coefficient contains the subdifferential operators of two convex functions (also called generalized backward doubly stochastic variational inequalities) are considered. By means of a penalization argument b...

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Bibliographic Details
Published in:arXiv.org 2011-08
Main Authors: Ren, Yong, Zhou, Qing, Auguste Aman
Format: Article
Language:English
Subjects:
Differential equations
Dirichlet problem
Economic models
Mathematical analysis
Neumann problem
Operators (mathematics)
Online Access:Get full text
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Summary:In this paper, a class of generalized backward doubly stochastic differential equations whose coefficient contains the subdifferential operators of two convex functions (also called generalized backward doubly stochastic variational inequalities) are considered. By means of a penalization argument based on Yosida approximation, we establish the existence and uniqueness of the solution. As an application, this result is used to derive existence result of stochastic viscosity solution for a class of multivalued stochastic Dirichlet-Neumann problems.
ISSN:2331-8422