Mean square stability of two classes of theta method for neutral stochastic differential delay equations

详细信息    查看全文

• 作者：Linna Liu^a ; Quanxin Zhu^a ; ^b ; ^{zqx22@126.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Neutral stochastic differential delay equation ; Mean square stability ; Exponential stability ; Stochastic linear theta method ; Split-step theta method
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2016
• 出版时间：15 October 2016
• 年：2016
• 卷：305
• 期：Complete
• 页码：55-67
• 全文大小：460 K

文摘

In this paper, a stochastic linear theta (SLT) method is introduced and analyzed for neutral stochastic differential delay equations (NSDDEs). We give some conditions on neutral item, drift and diffusion coefficients, which admit that the diffusion coefficient can be highly nonlinear and does not necessarily satisfy a linear growth or global Lipschitz condition. It is proved that, for all positive stepsizes, the SLT method with $\theta \in [\frac{1}{2},1]$ is asymptotically mean stable and so is $\theta \in [0,\frac{1}{2})$ under a stronger assumption. Furthermore, we consider the split-step theta (SST) method and obtain a similar but better result. That is, the SST method with $\theta \in [\frac{1}{2},1]$ is exponentially mean stable and so is $\theta \in [0,\frac{1}{2})$. Finally, two numerical examples are given to show the efficiency of the obtained results.