Mean-square stability of the backward Euler-Maruyama method for neutral stochastic delay differential equations with jumps
Mean-square stability of the backward Euler-Maruyama method for neutral stochastic delay differential equations with jumps
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带跳变的中性随机时滞微分方程后向 Euler-Maruyama 方法的均方稳定性
DOI：
10.1002/mma.4098
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发表时间：
2017
影响因子：
2.9
通讯作者：
Deng Feiqi
中科院分区：
文献类型：
--
作者：
Mo Haoyi;Zhao Xueyan;Deng Feiqi
本文主要考虑带跳跃的中立型随机延迟微分方程(NSDDEs)的均方稳定性是否与向后Euler-Maruyama方法的均方稳定性相同。在单边Lipschitz条件和线性增长条件下，利用泛函比较原理和Barbalat引理证明了带跳的NSDDEs的平凡解是均方稳定的。结果表明，在相同的条件下，反向Euler-Maruyama方法可以重现平凡解的均方稳定性。隐式后向Euler-Maruyama方法不需要漂移系数的线性增长条件，因而表现出比显式Euler-Maruyama方法更好的特性。与已有的一些结果相比，我们的结果不需要在中性部分增加额外的条件。结论适用于NSDDEs和带跳跃的SDDEs。通过算例说明了理论结果的有效性。版权所有©2016 John Wiley&Sons，Ltd.
This paper is mainly considered whether the mean‐square stability of neutral stochastic delay differential equations (NSDDEs) with jumps is shared with that of the backward Euler–Maruyama method. Under the one‐sided Lipschitz condition and the linear growth condition, the trivial solution of NSDDEs with jumps is proved to be mean‐square stable by using the functional comparison principle and the Barbalat's lemma. It is shown that the backward Euler–Maruyama method can reproduce the mean‐square stability of the trivial solution under the same conditions. The implicit backward Euler–Maruyama method shows better characteristic than the explicit Euler–Maruyama method for the reason that it works without the linear growth condition on the drift coefficient. Compared with some existing results, our results do not need to add extra condition on the neutral part. The conclusions can be applied to NSDDEs and SDDEs with jumps. The effectiveness of the theoretical results is illustrated by an example. Copyright © 2016 John Wiley & Sons, Ltd.