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.
出处
《应用数学》
CSCD
北大核心
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)
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
Stochastic delay differential equation
Markovian Switching
Euler method
One-sided Lipschitz condition
Polynomial growth condition
