The present research studies the boundedness issue of Lévy driven non-autonomous stochastic differential systems with mixed discrete and distributed delays. A set of sufficient conditions of the $p$th moment globally asymptotical boundedness is obtained by combining the Lyapunov function method with the inequality technique. The proposed results reveal that the convergence rate $\lambda$ and the coefficients of the estimates for Lyapunov function $W$ and Itô operator $\mathcal {L}W$ can determine the upper bound for the solution. The presented results are demonstrated by an illustrative example.

中文翻译：

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具有Lévy噪声和混合时滞的非自治随机微分系统的有界性分析

本研究研究具有混合离散和分布式时滞的Lévy驱动非自治随机微分系统的有界性问题。通过将Lyapunov函数方法与不等式技术相结合，获得了第一个$ p $矩全局渐近有界的一组充分条件。拟议的结果表明，收敛速度$ \ lambda $以及Lyapunov函数$ W $和Itô算子$ \ mathcal {L} W $的估计系数可以确定解的上限。给出的结果通过一个示例性例子进行了证明。