Asymptotic stability in the pth moment for stochastic differential equations with Levy noise
Asymptotic stability in the pth moment for stochastic differential equations with Levy noise
复制标题
带 Levy 噪声的随机微分方程的 p 阶矩渐近稳定性
DOI：
10.1016/j.jmaa.2014.02.016
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发表时间：
2014
影响因子：
1.3
通讯作者：
朱全新
中科院分区：
文献类型：
--
作者：
朱全新
本文致力于研究一类带有Lévy噪声的随机微分方程。与标准高斯噪声相比，Lévy 噪声更加通用且有趣，应用范围更广。然而，Lévy 噪声由于其样本路径的不连续性使得分析变得更加困难。在本文中，我们试图克服这个困难。我们提出了几个充分条件，在这些条件下我们研究解的长期行为，包括第矩矩的渐近稳定性和几乎确定稳定性。此外，我们还讨论了解的两种连续性：概率连续性和第 p 矩连续性。最后，我们提供了两个例子来说明理论结果的有效性。
This paper is devoted to study a class of stochastic differential equations with Lévy noise. In comparison to the standard Gaussian noise, Lévy noise is more versatile and interesting with a wider range of applications. However, Lévy noise makes the analysis more difficult owing to the discontinuity of its sample paths. In this paper, we attempt to overcome this difficulty. We propose several sufficient conditions under which we investigate the long-time behavior of the solution including the asymptotic stability in thepth moment and almost sure stability. Also, we discuss two types of continuity of the solution: continuous in probability and continuous in thepth moment. Finally, we provide two examples to illustrate the effectiveness of the theoretical results.