In order to study stochastic viscosity solutions for a class of semilinear stochastic integral-partial differential equations (SIPDEs), a new class of generalized backward doubly stochastic differential equations with general jumps is investigated. The definition of stochastic viscosity solutions of SIPDEs is introduced. A probabilistic representation for stochastic viscosity solutions of semilinear SIPDEs with nonlinear Neumann boundary conditions is given.

中文翻译：

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随机积分-偏微分方程的随机粘度解

为了研究一类半线性随机积分-偏微分方程（SIPDEs）的随机粘度解，研究了一类新的具有一般跳跃的广义后向双随机微分方程。介绍了SIPDEs的随机粘度解的定义。给出了具有非线性诺伊曼边界条件的半线性SIPDEs随机粘度解的概率表示。