中立型随机延迟微分方程分裂步θ方法的强收敛性

STRONG CONVERGENCE OF THE SPLIT-STEPθMETHOD FOR NEUTRAL STOCHASTIC DELAY DIFFERENTIAL EQUATIONS

中立型随机延迟微分方程常出现在一些科学技术和工程领域中.本文在漂移系数和扩散系数关于非延迟项满足全局Lipschitz条件,关于延迟项满足多项式增长条件以及中立项满足多项式增长条件下,证明了分裂步θ方法对于中立型随机延迟微分方程的强收敛阶为1/2.数值实验也验证了这一理论结果.

Neutral stochastic delay differential equations often appear in some fields of science and engineering.The aim of this article is to investigate the strong convergence of the split-stepθmethod for neutral stochastic delay differential equations.When the drift and diffusion coefficients satisfy global Lipschitz condition with respect to the present state and the polynomial growth condition about the delay term respectively,and the neutral term may also be polynomial growth,this method is shown to be strongly convergent of order 1/2.Some numerical results are presented to confirm the obtained theoretical results.