In this paper, we study the numerical method for solving forward-backward stochastic differential equations driven by $G$-Brownian motion ($G$-FBSDEs) which correspond to fully nonlinear partial differential equations (PDEs). First, we give an approximate conditional $G$-expectation and obtain feasible methods to calculate the distribution of $G$-Brownian motion. On this basis, some efficient numerical schemes for $G$-FBSDEs are then proposed. We rigorously analyze errors of the proposed schemes and prove the convergence results. Finally, several numerical experiments are given to demonstrate the accuracy of our method.
翻译：在本文中,我们研究了由美元-布朗运动(G$-FBSDEs)驱动的、完全非线性部分差异方程(PDEs)所驱动的解决前向后向的随机差异方程的数字方法。首先,我们给出了大约有条件的G$-布朗动议的预期,并获得了计算美元-布朗动议分布的可行方法。在此基础上,我们提出了一些高效的G$-FBSDEs数字方案。我们严格分析拟议办法的错误,并证明趋同结果。最后,我们进行了几项数字实验,以证明我们方法的准确性。
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