Abstract It is well known that stability is one of most important topics in economy and control. In this paper, we focus on the practical stability problem for a class of stochastic age-dependent (vintage) capital system with Levy noise. Compared with the classical Lyapunov stability theory, practical stability can depict not only qualitative behavior but also quantitative properties, such as specific trajectory bounds and specific transient behavior. With the help of the stochastic analysis theory and Ito’s formula, we establish some novel criteria for the mean square and almost sure practical exponential stability of the addressed system. The obtained results improve some previous works given in the literature. Moreover, an example is provided to illustrate the theoretical results.

中文翻译：

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具有 Lévy 噪声的随机年龄相关资本系统的实用指数稳定性

摘要 众所周知，稳定性是经济和控制中最重要的课题之一。在本文中，我们关注一类具有 Levy 噪声的随机年龄相关（年份）资本系统的实际稳定性问题。与经典的李雅普诺夫稳定性理论相比，实际稳定性不仅可以描述定性行为，还可以描述定量属性，例如特定的轨迹边界和特定的瞬态行为。在随机分析理论和伊藤公式的帮助下，我们为所寻址系统的均方和几乎确定的实际指数稳定性建立了一些新的标准。获得的结果改进了文献中给出的一些先前的工作。此外，还提供了一个例子来说明理论结果。