Multivalued stochastic Dirichlet-Neumann problems and generalized backward doubly stochastic differential equations
Probability
2011-08-04 v2
Abstract
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.
Cite
@article{arxiv.1011.3071,
title = {Multivalued stochastic Dirichlet-Neumann problems and generalized backward doubly stochastic differential equations},
author = {Yong Ren and Qing Zhou and Auguste Aman},
journal= {arXiv preprint arXiv:1011.3071},
year = {2011}
}
Comments
This version has been greatly improved, especially Section 5, and has been submitted for publication