论文标题
高阶组合多步方案，用于求解向后向后的随机微分方程
High-order combined Multi-step Scheme for solving forward Backward Stochastic Differential Equations
论文作者
论文摘要
在这项工作中，为了获得用于求解向后向后随机微分方程的高阶方案，我们采用了[W. Zhao，Y。Fu和T. Zhou，Siam J. Sci。 Comput。，36（4）（2014），pp.A1731-A1751]通过组合多步。两个包含条件期望及其导数的普通微分方程来自向后分量。这些衍生物通过具有多步组合的有限差异方法近似。最终的方案是涉及条件期望的时间方向上的半差异，通过在空间网格上使用高斯正交规则和多项式插值来解决。我们新提出的多步骤方案允许更高的收敛速率高达第九阶，并且更有效。最后，我们提供了所提出方法的收敛性的数值说明。
In this work, in order to obtain higher-order schemes for solving forward backward stochastic differential equations, we adopt the high-order multi-step method in [W. Zhao, Y. Fu and T. Zhou, SIAM J. Sci. Comput., 36(4) (2014), pp.A1731-A1751] by combining multi-steps. Two reference ordinary differential equations containing the conditional expectations and their derivatives are derived from the backward component. These derivatives are approximated by finite difference methods with multi-step combinations. The resulting scheme is a semi-discretization in the time direction involving conditional expectations, which are solved by using the Gaussian quadrature rules and polynomial interpolations on the spatial grids. Our new proposed multi-step scheme allows for higher convergence rate up to ninth order, and are more efficient. Finally, we provide a numerical illustration of the convergence of the proposed method.
