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

Yong Ren; Qing Zhou; Auguste Aman

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arXiv · 1011.3071

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

Yong Ren·Qing Zhou·Auguste Aman

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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.

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Yong Ren, Qing Zhou, Auguste Aman. 2011-08-03. Multivalued stochastic Dirichlet-Neumann problems and generalized backward doubly stochastic differential equations. https://arxiv.org/abs/1011.3071

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