Abstract and Applied Analysis
- Abstr. Appl. Anal.
- Volume 2012, Special Issue (2012), Article ID 831082, 13 pages.
Stability of Analytical and Numerical Solutions for Nonlinear Stochastic Delay Differential Equations with Jumps
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 when , and they are exponentially mean-square stable if the stepsize when . Finally, some numerical experiments are given to illustrate the theoretical results.
Abstr. Appl. Anal., Volume 2012, Special Issue (2012), Article ID 831082, 13 pages.
First available in Project Euclid: 1 April 2013
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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