非线性随机延迟微分方程Euler-Maruyama方法的收敛性  

Convergence of Euler-Maruyama Methods for Nonlinear Stochastic Delay Differential Equations

作　　者：王文强[1] 李寿佛[1] 黄山[1] 

机构地区：[1]湘潭大学数学与计算科学学院,湖南湘潭411105

出　　处：《系统仿真学报》2007年第17期3910-3913,共4页Journal of System Simulation

基　　金：国家自然科学基金资助项目(10271100);湖南省教育厅资助科研项目(06B091)

摘　　要：首先利用附近已有节点上的值通过插值对延迟项进行数值逼近,这是一种崭新的尝试;然后针对较一般情形下的一类非线性随机延迟微分方程初值问题,得到了带线性插值的Euler-Maruyama方法在均方意义下是收敛的理论结果,它部分推广了已有文献中的相关结论。The error analysis of Euler-Maruyama methods applying to a general class of nonlinear stochastic delay differential equations was concerned with. A new attempt to get the numerical approximation of the delay argument was proposed, i.e, the delay argument was solved by interpolating, It is proved that the Euler-Maruyama methods with linear interpolation procedure is convergent. Moreover, the results can be regarded as a partial extension of the similar conclusions in the present documents.

关 键 词：非线性随机延迟微分方程 EULER-MARUYAMA方法 插值 收敛性 

分 类 号：O241.81[理学—计算数学] O211.63[理学—数学]