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

Qiyong Li and Siqing Gan

Abstract and Applied Analysis, 2012, vol. 2012, issue 1

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

Date: 2012
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https://doi.org/10.1155/2012/831082

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:831082

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