Abstract and Applied Analysis

Stability of Analytical and Numerical Solutions for Nonlinear Stochastic Delay Differential Equations with Jumps

Qiyong Li and Siqing Gan

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Abstract

This paper is concerned with the stability of analytical and numerical solutions for nonlinear stochastic delay differential equations (SDDEs) with jumps. A sufficient condition for mean-square exponential stability of the exact solution is derived. Then, mean-square stability of the numerical solution is investigated. It is shown that the compensated stochastic θ methods inherit stability property of the exact solution. More precisely, the methods are mean-square stable for any stepsize Δ t = τ / m when 1 / 2 θ 1 , and they are exponentially mean-square stable if the stepsize Δ t ( 0 , Δ t 0 ) when 0 θ < 1 . Finally, some numerical experiments are given to illustrate the theoretical results.

Article information

Source
Abstr. Appl. Anal., Volume 2012, Special Issue (2012), Article ID 831082, 13 pages.

Dates
First available in Project Euclid: 1 April 2013

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1364845178

Digital Object Identifier
doi:10.1155/2012/831082

Mathematical Reviews number (MathSciNet)
MR2889088

Zentralblatt MATH identifier
1236.60055

Citation

Li, Qiyong; Gan, Siqing. Stability of Analytical and Numerical Solutions for Nonlinear Stochastic Delay Differential Equations with Jumps. Abstr. Appl. Anal. 2012, Special Issue (2012), Article ID 831082, 13 pages. doi:10.1155/2012/831082. https://projecteuclid.org/euclid.aaa/1364845178


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