The split-step backward Euler method for linear stochastic delay differential equations

被引：36
|
作者：
Zhang, Haomin [1 ]
Gan, Siqing [1 ]
Hu, Lin [1 ]
机构：
[1] Cent S Univ, Sch Math Sci & Comp Technol, Changsha 410075, Hunan, Peoples R China
来源：
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2009年 / 225卷 / 02期
关键词：
Stochastic delay differential equation; Split-step backward Euler method; Mean-square stability; General mean-square stability; Finite-time convergence; Numerical solution; STABILITY; CONVERGENCE;
D O I：
10.1016/j.cam.2008.08.032
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, the numerical approximation of solutions of linear stochastic delay differential equations (SDDEs) in the Ito sense is considered. We construct split-step backward Euler (SSBE) method for solving linear SDDEs and develop the fundamental numerical analysis concerning its strong convergence and mean-square stability. It is proved that the SSBE method is convergent with strong order gamma = 1/2 in the mean-square sense. The conditions under which the SSBE method is mean-square stable (MS-stable) and general mean-square stable (GMS-stable) are obtained. Some illustrative numerical examples are presented to demonstrate the order of strong convergence and the mean-square stability of the SSBE method. (c) 2008 Elsevier B.V. All rights reserved.
引用
收藏
页码：558 / 568
页数：11
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