Abstract In this work, we mainly explore the L 2 -regularity for the second component of the solutions to linear backward stochastic heat equations, which is crucial to obtain the convergence of the numerical solutions. As an application, we provide the convergence rate for time-discretized Galerkin approximation of these equations.

中文翻译：

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L2-线性后向随机热方程解的正则性及其数值应用

摘要 在这项工作中，我们主要探索线性反向随机热方程解的第二分量的L 2 -正则性，这对于获得数值解的收敛性至关重要。作为一个应用，我们提供了这些方程的时间离散伽辽金近似的收敛速度。