求解随机微分方程split-step欧拉方法的收敛性

Convergence of the Split-step Euler Methods for Stochastic Differential Equations

给出随机微分方程的split-step欧拉格式的算法,并证明了当方程的偏移系数和扩散系数均满足线性增长条件和李普希兹条件的情况下,此方法用以求解随机微分方程的收敛性,并且求出强收敛的阶是1/2.同时证明了split-step近似解的均方收敛理论.

The split-step Euler scheme for SDEs is first brought forward, under Lipschitz and linear growth condi-tion it is proved that the split-step Euler scheme is convergence with strong order1/2.At the same time, the mean-square stability of the theory of split-step Euler-approximation is proved.