论文标题
由$ g $ -Brownian Motion驱动的前向后随机微分方程的有效数值方法
An Efficient Numerical Method for Forward-Backward Stochastic Differential Equations Driven by $G$-Brownian motion
论文作者
论文摘要
在本文中，我们研究了通过$ g $ -Brownian运动（$ G $ -FBSDE）驱动的前向后随机微分方程的数值方法，该方程对应于完全非线性的部分偏微分方程（PDES）。首先，我们提供了近似条件的$ g $ - 预测，并获得可行的方法来计算$ g $ -Brownian Motion的分布。在此基础上，提出了一些针对$ g $ -FBSDE的有效数值方案。我们严格地分析了提出的方案的错误，并证明了收敛结果。最后，进行了一些数值实验，以证明我们方法的准确性。
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.
