TY - JOUR A2 - Zhang, Guang AU - Yuan, Haiyan AU - Shen, Jihong AU - Song, Cheng PY - 2016 DA - 2016/08/07 TI - On Mean Square Stability and Dissipativity of Split-Step Theta Method for Nonlinear Neutral Stochastic Delay Differential Equations SP - 7397941 VL - 2016 AB - 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. SN - 1026-0226 UR - https://doi.org/10.1155/2016/7397941 DO - 10.1155/2016/7397941 JF - Discrete Dynamics in Nature and Society PB - Hindawi Publishing Corporation KW - ER -