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

Haiyan Yuan, Jihong Shen and Cheng Song

Discrete Dynamics in Nature and Society, 2016, vol. 2016, issue 1

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 θ ∈ (1/2, 1] is asymptotically mean square stable for all positive step sizes, and the split‐step theta method with θ ∈ [0, 1/2] 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.

Date: 2016
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https://doi.org/10.1155/2016/7397941

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnddns:v:2016:y:2016:i:1:n:7397941

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