In this paper, we propose an explicit second-order scheme for solving decoupled mean-field forward backward stochastic differential equations. Its stability is theoretically proved, and its error estimates are rigorously deduced, which show that the proposed scheme is of second-order accurate when the weak-order 2.0 Itô-Taylor scheme is used to solve mean-field stochastic differential equations. Some numerical experiments are presented to verify the theoretical results.

中文翻译：

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均值场正向后向随机微分方程的显式二阶数值格式

在本文中，我们提出了一个明确的二阶格式，用于解耦的平均场正向后向随机微分方程。理论上证明了其稳定性，并严格推导了其误差估计值，这表明当使用弱阶2.0Itô-Taylor方案求解平均场随机微分方程时，该方案具有二阶精度。进行了一些数值实验以验证理论结果。