In this paper, we present a numerical scheme to solve the initial-boundary value problem for backward stochastic partial differential equations of parabolic type. Based on the Galerkin method, we approximate the original equation by a family of backward stochastic differential equations (BSDEs, for short), and then solve these BSDEs by the time discretization. Combining the truncation with respect to the spatial variable and the backward Euler method on time variable, we obtain the global $L^2$ error estimate.

中文翻译：

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后向随机抛物线微分方程的半离散伽辽金格式

在本文中，我们提出了一种求解抛物型后向随机偏微分方程初边值问题的数值方案。基于伽辽金方法，我们通过一族后向随机微分方程（简称BSDEs）来逼近原方程，然后通过时间离散化来求解这些BSDEs。结合空间变量的截断和时间变量的后向欧拉方法，我们得到全局$L^2$误差估计。