论文标题
使用小差异操作员的无限尺寸符号的向后随机微分方程（BSDE）
Backward Stochastic Differential Equations (BSDEs) Using Infinite-dimensional Martingales with Subdifferential Operator
论文作者
论文摘要
在本文中，我们专注于一个向后的随机微分方程（BSDE）家族，其子分别算子由无限尺寸的martingales驱动，涉及对称性，即，该过程涉及一个积极的确定核操作员q。我们将展示这种对这种Infinite-dimente二维BSDES BSDES EXISTS的解决方案。使用Yosida近似值建立溶液的存在，并使用固定点定理证明了唯一性。此外，作为主要结果的应用，我们将表明，由无限二维martingales驱动的向后随机部分微分方程具有连续线性操作员在函数f等于零的条件下具有独特的解决方案。
In this paper, we focus on a family of backward stochastic differential equations (BSDEs) with sub-differential operators that are driven by infinite-dimensional martingales which involve symmetry, that is, the process involves a positive definite nuclear operator Q. We shall show that the solution to such infinite-dimensional BSDEs exists and is unique. The existence of the solution is established using Yosida approximations, and the uniqueness is proved using Fixed Point Theorem. Furthermore, as an application of the main result, we shall show that the backward stochastic partial differential equation driven by infinite-dimensional martingales with a continuous linear operator has a unique solution under the condition that the function F equals to zero.
