Split-step theta method for stochastic delay integro-differential equations with mean square exponential stability
Split-step theta method for stochastic delay integro-differential equations with mean square exponential stability
复制标题
具有均方指数稳定性的随机时滞积分微分方程的分步theta方法
DOI：
10.1016/j.amc.2019.01.073
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发表时间：
2019
影响因子：
4
通讯作者：
Deng Feiqi
中科院分区：
文献类型：
--
作者：
Liu Linna;Mo Haoyi;Deng Feiqi
在本文中，我们通过拉格朗日插值技术提出了随机延迟积分微分方程的分步theta方法，并研究了该方案的均方指数稳定性。结果表明，分步theta方法可以继承连续模型在线性增长条件下的均方指数稳定性以及本文建立的延迟微分和差分不等式所提出的稳定性条件。论文最后给出了一个数值例子来说明论文的方法和结论。另外，附录中证明了分步theta方法的收敛性。
In this paper, we propose the split-step theta method for stochastic delay integro-differential equations by the Lagrange interpolation technique and investigate the mean square exponential stability of the proposed scheme. It is shown that the split-step theta method can inherit the mean square exponential stability of the continuous model under the linear growth condition and the proposed stability condition by the delayed differential and difference inequalities established in the paper. A numerical example is given at the end of the paper to illustrate the method and conclusion of the paper. In addition, the convergence of the split-step theta method is proved in the Appendix.