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Mean-Square Convergence of Drift-Implicit One-Step Methods for Neutral Stochastic Delay Differential Equations with Jump Diffusion

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  • Lin Hu
  • Siqing Gan

Abstract

A class of drift-implicit one-step schemes are proposed for the neutral stochastic delay differential equations (NSDDEs) driven by Poisson processes. A general framework for mean-square convergence of the methods is provided. It is shown that under certain conditions global error estimates for a method can be inferred from estimates on its local error. The applicability of the mean-square convergence theory is illustrated by the stochastic θ-methods and the balanced implicit methods. It is derived from Theorem 3.1 that the order of the mean-square convergence of both of them for NSDDEs with jumps is 1/2. Numerical experiments illustrate the theoretical results. It is worth noting that the results of mean-square convergence of the stochastic θ-methods and the balanced implicit methods are also new.

Suggested Citation

  • Lin Hu & Siqing Gan, 2011. "Mean-Square Convergence of Drift-Implicit One-Step Methods for Neutral Stochastic Delay Differential Equations with Jump Diffusion," Discrete Dynamics in Nature and Society, Hindawi, vol. 2011, pages 1-22, November.
    • Handle: RePEc:hin:jnddns:917892
    DOI: 10.1155/2011/917892
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