用于前向后向随机微分方程的新型一步二阶方案

Qiang Han, Shihao Lan, Quanxin Zhu
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摘要

在本文中,我们以 Crank-Nicolson 方法作为我们提出的框架中的一个具体实例,提出了一种新颖的一步求解前向后向随机微分方程的显式二阶方案。我们首先给出了一个严格的稳定性结果,然后给出了精确的误差估计,证实所提出的新方案实现了二阶收敛。数值实验支持了所提方法的理论结果。
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A novel second order scheme with one step for forward backward stochastic differential equations
In this paper, we present a novel explicit second order scheme with one step for solving the forward backward stochastic differential equations, with the Crank-Nicolson method as a specific instance within our proposed framework. We first present a rigorous stability result, followed by precise error estimates that confirm the proposed novel scheme achieves second-order convergence. The theoretical results for the proposed methods are supported by numerical experiments.
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