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

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  • Qiyong Li
  • Siqing Gan

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 when , and they are exponentially mean-square stable if the stepsize when . Finally, some numerical experiments are given to illustrate the theoretical results.

Suggested Citation

  • Qiyong Li & Siqing Gan, 2012. "Stability of Analytical and Numerical Solutions for Nonlinear Stochastic Delay Differential Equations with Jumps," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-13, February.
    • Handle: RePEc:hin:jnlaaa:831082
    DOI: 10.1155/2012/831082
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