New criteria on asymptotic behavior of neutral stochastic functional differential equations
New criteria on asymptotic behavior of neutral stochastic functional differential equations
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DOI：
10.1016/j.automatica.2012.11.045
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发表时间：
2013-02
期刊：
影响因子：
--
通讯作者：
Yinfang Song;Yi Shen
中科院分区：
文献类型：
--
作者：
Yinfang Song;Yi Shen
本文研究了中性型随机泛函微分方程在局部Lipschitz条件和依赖于扩散算子和矫顽力项的条件下的渐近行为，该渐近行为比经典增长条件更为普遍。利用Lyapunov分析方法和一些随机分析技术，得到了NSFDEs具有一般衰减率和有界性的稳定性的充分条件。我们的结果不仅涵盖了一类广泛的高度非线性NSFDEs，而且还可以处理一般的稳定性问题，包括多项式稳定性和指数稳定性。最后，通过实例验证了理论结果的有效性。
This paper investigates the asymptotic behavior of neutral stochastic functional differential equations (NSFDEs) under both the local Lipschitz condition and the one dependent on the diffusion operator and on a coercivity term, which is more general than the classical growth condition. Some sufficient conditions for stability with general decay rate and boundedness of NSFDEs are derived via the Lyapunov analysis method and some stochastic analysis techniques. Our results not only cover a wide class of highly nonlinear NSFDEs but they can also deal with general stability issues including the polynomial stability and the exponential stability. Finally, an illustrative example is provided to show the effectiveness of our theoretical results.