Novel multi-step predictor-corrector numerical schemes have been derived for approximating decoupled forward-backward stochastic differential equations (FBSDEs). The stability and high order rate of convergence of the schemes are rigorously proved. We also present a sufficient and necessary condition for the stability of the schemes. Numerical experiments are given to illustrate the stability and convergence rates of the proposed methods.

翻译：已经为近似前向后向前向的随机差分方程式(FBSDEs)制定了新的多步预测-校正数字办法,这些办法的稳定性和高顺序趋同率得到了严格证明,我们还为这些办法的稳定提供了充分和必要的条件,并进行了数值实验,以说明拟议方法的稳定性和趋同率。