非李普希兹条件下马尔科夫调制随机延迟微分方程数值解的收敛性（英文）  

Convergence of Numerical Solutions to Stochastic Delay Differential Equations with Markovian Swithing Under Non-Lipschitz Conditions

作　　者：范振成 

机构地区：[1]闽江学院数学研究所,福建福州350108

出　　处：《应用数学》2017年第4期874-881,共8页Mathematica Applicata

基　　金：Supported by the Natural Science Foundation of Fujian Province(2015J01588);the Science Project Municipal University of Fujian Province(JK2014041)

摘　　要：在全局李普希兹条件下,已经建立了马尔科夫调制的随机微分方程的欧拉方法.然而对于实际系统,全局李普希兹条件通常不成立.在本文中,在弱于全局李普希兹条件的条件下,我们证明马尔科夫调制的随机微分方程的欧拉方法是收敛的,并且其收敛阶和全局李普希兹条件下相同.The Euler scheme of the stochastic delay differential equations with Markovian switching （SDDEwMS） has been developed under the global Lipschitz （GL） condition. However the GL condition is often not met by systems of interest. In this paper, we prove that under certain conditions, weaker than the GL condition, and the Euler scheme applied to SDDEwMS is convergent with the same order of accuracy as the Euler method under the CL condition.

关 键 词：随机延迟微分方程 马尔科夫调制 欧拉方法 单边李普希兹条件 多项式增长条件 

分 类 号：O211.63[理学—概率论与数理统计]