Partial practical stability and asymptotic stability of stochastic differential equations driven by l?evy noise with a general decay rate

In this paper, we mainly study the almost sure partial practical stability of stochastic differential equations driven by Le ' vy noise with a general decay rate. By establishing a suitable Lyapunov function and using Exponen-tial Martingale inequality and Borel-Cantelli theorem, giving some sufficient conditions that can guarantee the almost sure partial practical stability of equations. At the same time, we also study general conditions that guarantee the almost sure asymptotic stability of the equation. Finally, we also give two examples to illustrate our theoretical results.