Convergence of numerical solutions to stochastic differential delay equations with Poisson jump and Markovian switching

被引：15

作者：

Wang, La-Sheng ^{[1
]}

Xue, Hong

机构：

[1] Xian Jiaotong Univ, Fac Sci, Xian 710049, Peoples R China

[2] Xian Polytech Univ, Fac Sci, Xian 710048, Peoples R China

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2007年 / 188卷 / 02期

基金：

中国国家自然科学基金;

关键词：

Markovian switching; Poisson jump; Euler scheme; local lipschitz condition;

D O I：

10.1016/j.amc.2006.10.058

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In general stochastic delay different equations with Poisson jump and Markovian switching do not have explicit solutions. Appropriate numerical approximations, such as the Euler scheme, are therefore a vital tool in exploring their properties. Unfortunately, the numerical methods for stochastic delay differential equations with Poisson jump and Markovian switching (SDDEwPJMSs), have never been studied. In this paper we proved that the Euler approximate solutions will converge to the exact solutions for SDDEwPJMSs under local Lipschitz condition. This result is more general than what they deal with the Markovian switching term or the jump term. (c) 2006 Elsevier Inc. All rights reserved.

引用

页码：1161 / 1172

页数：12

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