Stochastic Viscosity Solutions for SPDEs with Discontinuous Coefficients

• 作者: Yidong Zhang
• 来源期刊: 应用数学(英文)
• 学科: 数学
• 关键词: Stochastic Partial Differential Equation Stochastic Viscosity Solution Backward Doubly Stochastic Differential Equation
• 年，卷（期）: 2020,（11）
• 页码范围: 1219-1228
• 页数: 10页
• 分类号: O17

摘要

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 <em>f</em>_<em>n</em> to the coefficient <em>f</em>, 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.