线性随机时滞微分方程裂步Milstein方法的收敛性(英文)  

Convergence of split-step Milstein method for linear stochastic delay differential equations

作　　者：郭谦[1] 解雯雯[1] 陶雪银[1] 朱颖[2] 

机构地区：[1]上海师范大学数理学院,上海200234 [2]上海师范大学人文与传播学院,上海200234

出　　处：《应用数学与计算数学学报》2012年第4期456-464,共9页Communication on Applied Mathematics and Computation

基　　金：supported by the National Natural Science Foundation of China(10901106);the Natural Science Foundation of Shanghai Municipality,China(09ZR1423200);the Innovation Program of Shanghai Municipal Education Commission(09YZ150);the E-Institutes of Shanghai Municipal Education Commission(E03004);the Shanghai Leading Academic Discipline Project(S30405)

摘　　要：给出一个新的求解线性随机时滞微分方程的显式分裂步长Milstein格式.运用ItoTaylor展开式证明该格式相对于已有的求解随机时滞微分方程的分裂步长方法而言具有更好的收敛性.数值实验验证了理论分析的正确性.A new explicit split-step Milstein method for solving linear Ito stochastic differential equations （SDEs） with a constant time delay is introduced. The Ito-Taylor expansion is employed to prove the strong convergence, which inproves the convergence results of known split-step methods for stochastic delay differential equations （SDDEs）. Numerical experiments confirm the theoretical results.

关 键 词：随机时滞微分方程 Milstein格式 分裂步长 强收敛 

分 类 号：O211.63[理学—概率论与数理统计]