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

作者：Hu, Lin; Gan, Siqing^*

来源：Discrete Dynamics in Nature and Society, 2011, 2011(Pt.3): 917892.

DOI：10.1155/2011/917892

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 theta-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 theta-methods and the balanced implicit methods are also new.

• 出版日期2011
• 单位东北林业大学; 中南大学