Stability analysis of stochastic delay differential equations with Markovian switching driven by Lévy noise

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