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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 Δt = τ/m when 1/2 ≤ θ ≤ 1, and they are exponentially mean‐square stable if the stepsize Δt ∈ (0, Δt0) when 0 ≤ θ

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, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:831082
    DOI: 10.1155/2012/831082
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    References listed on IDEAS

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    1. Nicola Bruti-Liberati & Eckhard Platen, 2007. "Approximation of jump diffusions in finance and economics," Computational Economics, Springer;Society for Computational Economics, vol. 29(3), pages 283-312, May.
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    Cited by:

    1. Shifang Kuang & Yunjian Peng & Feiqi Deng & Wenhua Gao, 2013. "Exponential Stability and Numerical Methods of Stochastic Recurrent Neural Networks with Delays," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).

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