A Class of Stochastic Nonlinear Delay System with Jumps
A Class of Stochastic Nonlinear Delay System with Jumps
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一类带跳跃的随机非线性时滞系统
DOI：
10.1155/2014/458306
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发表时间：
2014
影响因子：
--
通讯作者：
Zhao Wenju
中科院分区：
文献类型：
--
作者：
Bai Ling;Zhang Kai;Zhao Wenju
研究非线性时滞微分系统的随机抑制与镇定问题。假设系统满足局部Lipschitz条件和单侧多项式增长条件。由于该系统在有限时间内可能爆炸，我们通过引入独立的布朗噪声和Levy噪声反馈随机扰动该系统。本文的贡献如下。(a)我们证明了在适当的参数下，布朗噪声或Levy噪声可以抑制解的潜在爆炸。(b)利用带跳的指数鞅不等式，讨论了样本李雅普诺夫指数非正的情况。(c)考虑线性Levy过程，利用局部鞅的强大数定律，给出了a.s.在定理13中研究了指数稳定性。
We consider stochastic suppression and stabilization for nonlinear delay differential system. The system is assumed to satisfy local Lipschitz condition and one-side polynomial growth condition. Since the system may explode in a finite time, we stochastically perturb this system by introducing independent Brownian noises and Levy noise feedbacks. The contributions of this paper are as follows. (a) We show that Brownian noises or Levy noise may suppress potential explosion of the solution for some appropriate parameters. (b) Using the exponential martingale inequality with jumps, we discuss the fact that the sample Lyapunov exponent is nonpositive. (c) Considering linear Levy processes, by the strong law of large number for local martingale, sufficient conditions for a.s. exponentially stability are investigated in Theorem 13.