Stability with general decay rate of hybrid neutral stochastic pantograph differential equations driven by Lévy noise

This paper focuses on the \begin{document}$ p $\end{document} th moment and almost sure stability with general decay rate (including exponential decay, polynomial decay, and logarithmic decay) of highly nonlinear hybrid neutral stochastic pantograph differential equations driven by L \begin{document}$ \acute{e} $\end{document} vy noise (NSPDEs-LN). The crucial techniques used are the Lyapunov functions and the nonnegative semi-martingale convergence theorem. Simultaneously, the diffusion operators are permitted to be controlled by several additional functions with time-varying coefficients, which can be applied to a broad class of the non-autonomous hybrid NSPDEs-LN with highly nonlinear coefficients. Besides, \begin{document}$ H_\infty $\end{document} stability and the almost sure asymptotic stability are also concerned. Finally, two examples are offered to illustrate the validity of the obtained theory.