一种基于随机Taylor展开式的随机微分方程数值解法  

A Kind of Numerical Method for Solving Stochastic Differential Equations Based on Stochastic Taylor Expansion

作　　者：李井刚[1] 朱晓临[1] 王子洁[1] 

机构地区：[1]合肥工业大学数学学院,安徽合肥230009

出　　处：《大学数学》2013年第4期44-51,共8页College Mathematics

基　　金：教育部科学技术研究重大项目(309017);安徽省自然科学基金(11013606M06);第38批留学回国人员科研启动基金(2010JYLH0322)

摘　　要：给出了一种基于随机Taylor展开式的随机微分方程数值格式,证明了它的均方稳定性。此外,还证明了这种数值格式的均值意义下的局部收敛阶为2,均方意义下的局部收敛阶为1,均方强收敛阶为1.数值实验表明本文的方法比Euler法和Milstein方法具有更好的逼近效果.A kind of numerical method for solving stochastic differential equations based on stochastic Taylor expansion is presented in this paper and its mean square stability is proved. For this method, this paper gives that the order of its local convergence in mean is 2, the order of its local convergence in mean square is 1 ; and the order of its strong convergence in mean square is 1. The numerical experiment shows that the method introduced in this paper is more accurate than Euler method and Milstein method.

关 键 词：Itó型随机微分方程 随机Taylor展开式 均方稳定 局部收敛阶 强收敛阶 

分 类 号：O211.63[理学—概率论与数理统计]