Stochastic Viscosity Solutions for SPDEs with Discontinuous Coefficients

Yidong Zhang

College of Science, North China University of Technology, Beijing, China.

DOI: 10.4236/am.2020.1111083                

Abstract

In this paper, a class of nonlinear stochastic partial differential equations with discontinuous coefficients is investigated. This study is motivated by some research on stochastic viscosity solutions under non-Lipschitz conditions recently. By studying the solutions of backward doubly stochastic differential equations with discontinuous coefficients and constructing a new approximation function f_n to the coefficient f, we get the existence of stochastic viscosity sub-solutions (or super-solutions).The results of this paper can be seen as the extension and application of related articles.

Keywords

Stochastic Partial Differential Equation, Stochastic Viscosity Solution, Backward Doubly Stochastic Differential Equation

Conflicts of Interest

The author declares no conflicts of interest regarding the publication of this paper.

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