Split-step theta method for stochastic delay integro-differential equations with mean square exponential stability

被引：11

作者：

Liu, Linna ^{[1
]}

Mo, Haoyi ^{[2
]}

Deng, Feiqi ^{[1
]}

机构：

[1] South China Univ Technol, Sch Automat Sci & Engn, Guangzhou 510640, Guangdong, Peoples R China

[2] Guangdong Univ Technol, Sch Appl Math, Guangzhou 510006, Guangdong, Peoples R China

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2019年 / 353卷

基金：

中国国家自然科学基金;

关键词：

Stochastic differential equations; Delay; Integro-differential equations; Split-step theta method; Mean square exponential stability; Convergence; MILSTEIN METHOD;

D O I：

10.1016/j.amc.2019.01.073

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we propose the split-step theta method for stochastic delay integro-differential equations by the Lagrange interpolation technique and investigate the mean square exponential stability of the proposed scheme. It is shown that the split-step theta method can inherit the mean square exponential stability of the continuous model under the linear growth condition and the proposed stability condition by the delayed differential and difference inequalities established in the paper. A numerical example is given at the end of the paper to illustrate the method and conclusion of the paper. In addition, the convergence of the split-step theta method is proved in the Appendix. (C) 2019 Elsevier Inc. All rights reserved.

引用

页码：320 / 328

页数：9

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