Partial practical stability and asymptotic stability of stochastic differential equations driven by Lévy noise with a general decay rate. (English) Zbl 07919807
Summary: In this paper, we mainly study the almost sure partial practical stability of stochastic differential equations driven by Lévy noise with a general decay rate. By establishing a suitable Lyapunov function and using Exponential 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.
MSC:
| 60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |
| 60G51 | Processes with independent increments; Lévy processes |
Keywords:
partial practical stability; Lévy noise; stochastic differential equations; Lyapunov functions; exponential Martingale inequalityReferences:
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