Convergence and stability of the semi-implicit Euler method for linear stochastic delay integro-differential equations

被引：30

作者：

Ding, Xiaohua ^{[1
]}

Wu, Kaining ^{[1
]}

Liu, Mingzhu ^{[1
]}

机构：

[1] Harbin Inst Technol, Dept Math, Weihai 264209, Peoples R China

来源：

INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS | 2006年 / 83卷 / 10期

关键词：

stochastic delay integro-differential equations; mean square stability; semi-implicit Euler method; numerical solution;

D O I：

10.1080/00207160601073680

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper deals with the convergence and stability of the semi-implicit Euler method for linear stochastic delay integro-differential equations. It is proved that the semi-implicit Euler method is convergent with strong order p = 0.5. The condition under which the method is asymptotic mean square stable is determined and numerical experiments are presented.

引用

页码：753 / 763

页数：11

共 17 条

[1] Baker C. T. H., 2000, Electronic Transactions on Numerical Analysis, V11
[2] Introduction to the numerical analysis of stochastic delay differential equations
Buckwar, E
[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2000, 125 (1-2) : 297 - 307
[3] Some peculiarities of the general method of Lyapunov functionals construction
Kolmanovskii, V
Shaikhet, L
[J]. APPLIED MATHEMATICS LETTERS, 2002, 15 (03) : 355 - 360
[4] Stability of θ-methods for delay integro-differential equations
Koto, T
[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2003, 161 (02) : 393 - 404
[5] Convergence and stability of the semi-implicit Euler method for a linear stochastic differential delay equation
Liu, MZ
Cao, WR
Fan, ZC
[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2004, 170 (02) : 255 - 268
[6] Mao X., 1997, Stochastic Differential Equations and Applications
[7] Mao X., 1994, EXPONENTIAL STABILIT
[8] Razumikhin-type theorems on exponential stability of stochastic functional differential equations
Mao, XR
[J]. STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 1996, 65 (02) : 233 - 250
[9] TIME DISCRETE TAYLOR APPROXIMATIONS FOR ITO PROCESSES WITH JUMP COMPONENT
MIKULEVICIUS, R
PLATEN, E
[J]. MATHEMATISCHE NACHRICHTEN, 1988, 138 : 93 - 104
[10] Milstein G., 1995, Numerical Integration of Stochastic Differential Equations, Mathematics and its Application

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