Stochastic Viscosity Solutions for SPDEs with Discontinuous Coefficients

Yidong  Zhang

doi:10.4236/am.2020.1111083

Yidong Zhang

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 fn 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

Cite this paper: Zhang, Y. (2020) Stochastic Viscosity Solutions for SPDEs with Discontinuous Coefficients. Applied Mathematics, 11, 1219-1228. doi: 10.4236/am.2020.1111083.

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