Stability analysis for stochastic Volterra–Levin equations with Poisson jumps: Fixed point approach
Stability analysis for stochastic Volterra–Levin equations with Poisson jumps: Fixed point approach
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DOI：
10.1063/1.3573598
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发表时间：
2011-04
影响因子：
1.3
通讯作者：
L. Guo;Quanxin Zhu
中科院分区：
文献类型：
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作者：
L. Guo;Quanxin Zhu
研究了一类带Poisson跳的随机Volterra-Levin方程.据作者所知，直到现在，这类新系统的稳定性问题还没有得到解决，因为泊松跳跃被认为是。本文的主要目的是填补这一差距。利用不动点理论，我们首先研究了所考虑系统解的存在唯一性以及p阶矩指数稳定性。然后利用Borel-Cantelli引理证明了该解几乎必然是p阶矩指数稳定的。我们的结果改进和推广了以往文献中的结果。最后，通过两个简单的例子说明了所得结果的有效性。
This paper is devoted to investigate a class of stochastic Volterra–Levin equations with Poisson jumps. To the best of the authors’ knowledge, till now, the stability problem for this class of new systems has not yet been solved since Poisson jumps are considered. The main objective of this paper is to fill the gap. By using the fixed point theory, we first study the existence and uniqueness of the solution as well as the pth moment exponential stability for the considered system. Then based on the well known Borel–Cantelli lemma, we prove that the solution is almost surely pth moment exponentially stable. Our results improve and generalize those given in the previous literature. Finally, two simple examples are provided to illustrate the effectiveness of the obtained results.