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On Mean Square Stability and Dissipativity of Split-Step Theta Method for Nonlinear Neutral Stochastic Delay Differential Equations

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  • Haiyan Yuan
  • Jihong Shen
  • Cheng Song

Abstract

A split-step theta (SST) method is introduced and used to solve the nonlinear neutral stochastic delay differential equations (NSDDEs). The mean square asymptotic stability of the split-step theta (SST) method for nonlinear neutral stochastic delay differential equations is studied. It is proved that under the one-sided Lipschitz condition and the linear growth condition, the split-step theta method with is asymptotically mean square stable for all positive step sizes, and the split-step theta method with is asymptotically mean square stable for some step sizes. It is also proved in this paper that the split-step theta (SST) method possesses a bounded absorbing set which is independent of initial data, and the mean square dissipativity of this method is also proved.

Suggested Citation

  • Haiyan Yuan & Jihong Shen & Cheng Song, 2016. "On Mean Square Stability and Dissipativity of Split-Step Theta Method for Nonlinear Neutral Stochastic Delay Differential Equations," Discrete Dynamics in Nature and Society, Hindawi, vol. 2016, pages 1-8, August.
    • Handle: RePEc:hin:jnddns:7397941
    DOI: 10.1155/2016/7397941
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