MEAN SQUARE STABILITY AND DISSIPATIVITY OF SPLIT- STEP THETA METHOD FOR NONLINEAR NEUTRAL STOCHASTIC DELAY DIFFERENTIAL EQUATIONS WITH POISSON JUMPS  

作　　者：Haiyan Yuan Jihong Shen Cheng Song 

机构地区：[1]Department of Mathematics, Heilongjiang Institute of Technology, Harbin 150050, China [2]Department of Mathematics, Harbin Engineering University, Harbin 150050, China [3]Department of Management, Harbin Institute University, Harbin 150001, China

出　　处：《Journal of Computational Mathematics》2017年第6期766-779,共14页计算数学（英文）

摘　　要：In this paper, a split-step 0 （SST） method is introduced and used to solve the non- linear neutral stochastic differential delay equations with Poisson jumps （NSDDEwPJ）. The mean square asymptotic stability of the SST method for nonlinear neutral stochastic differential equations with Poisson jumps is studied. It is proved that under the one-sided Lipschitz condition and the linear growth condition, the SST method with ∈ E （0, 2 -√2） is asymptotically mean square stable for all positive step sizes, and the SST method with ∈ E （2 -√2, 1） is asymptotically mean square stable for some step sizes. It is also proved in this paper that the SST method possesses a bounded absorbing set which is independent of initial data, and the mean square dissipativity of this method is also proved.In this paper, a split-step 0 （SST） method is introduced and used to solve the non- linear neutral stochastic differential delay equations with Poisson jumps （NSDDEwPJ）. The mean square asymptotic stability of the SST method for nonlinear neutral stochastic differential equations with Poisson jumps is studied. It is proved that under the one-sided Lipschitz condition and the linear growth condition, the SST method with ∈ E （0, 2 -√2） is asymptotically mean square stable for all positive step sizes, and the SST method with ∈ E （2 -√2, 1） is asymptotically mean square stable for some step sizes. It is also proved in this paper that the SST method possesses a bounded absorbing set which is independent of initial data, and the mean square dissipativity of this method is also proved.

关 键 词：Neutral stochastic delay differential equations Split-step method Stability Poisson jumps. 

分 类 号：O211.63[理学—概率论与数理统计] TP13[理学—数学]