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

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

2010-11-12

arxiv.org/abs/1011.3071v2

Mathematics

Probability

This version has been greatly improved, especially Section 5, and has been submitted for publication

Scientific paper

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.

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