<p style='text-indent:20px;'>In this paper, the existence and uniquenesss, stability analysis for stochastic delay differential equations with Markovian switching driven by L<inline-formula><tex-math>\begin{document}$ \acute{e} $\end{document}</tex-math></inline-formula>vy noise are studied. The existence and uniqueness of such equations is simply shown by using the Picard iterative methodology. By using the generalized integral, the Lyapunov-Krasovskii function and the theory of stochastic analysis, the exponential stability in <inline-formula><tex-math>\begin{document}$ p $\end{document}</tex-math></inline-formula>th(<inline-formula><tex-math>\begin{document}$ p\geq2 $\end{document}</tex-math></inline-formula>) for stochastic delay differential equations with Markovian switching driven by L<inline-formula><tex-math>\begin{document}$ \acute{e} $\end{document}</tex-math></inline-formula>vy noise is firstly investigated. The almost surely exponential stability is also applied. Finally, an example is provided to verify our results derived.</p>

中文翻译：

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L${\acute{e}}$vy 噪声驱动的马尔可夫切换随机延迟微分方程的稳定性分析

<p style='text-indent:20px;'>本文对L<inline-formula><tex-math>\begin{document}驱动的马尔可夫切换随机时滞微分方程的存在唯一性、稳定性分析$ \acute{e} $\end{document}</tex-math></inline-formula>vy 噪声进行了研究。这些方程的存在性和唯一性通过使用 Picard 迭代方法简单地显示出来。通过使用广义积分、Lyapunov-Krasovskii 函数和随机分析理论，<inline-formula><tex-math>\begin{document}$ p $\end{document}</tex-math 中的指数稳定性></inline-formula>th(<inline-formula><tex-math>\begin{document}$ p\geq2 $\end{document}</tex-math></inline-formula> ) 用于由 L<inline-formula><tex-math>\begin{document}$ \acute{e} $\end{document}</tex-math></inline-formula 驱动的马尔可夫切换的随机延迟微分方程>vy 噪声首先被研究。几乎可以肯定的指数稳定性也适用。最后，提供一个例子来验证我们得出的结果。</p>