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Asymptotic stability of stochastic differential equations driven by Lévy noise. (English) Zbl 1185.60058
Summary: Using key tools such as Itô’s formula for general semimartingales, Kunita’s moment estimates for Lévy-type stochastic integrals, and the exponential martingale inequality, we find conditions under which the solutions to the stochastic differential equations (SDEs) driven by Lévy noise are stable in probability, almost surely and moment exponentially stable.

##### MSC:
 60H10 Stochastic ordinary differential equations (aspects of stochastic analysis) 60G51 Processes with independent increments; Lévy processes 93D20 Asymptotic stability in control theory 93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, $$L^p, l^p$$, etc.) in control theory
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