Asymptotic Stability of Stochastic Differential Equations Driven by Lévy Noise
نویسنده
چکیده
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. Keywords; stochastic differential equation, Lévy noise, Poisson random measure, Brownian motion, almost sure asymptotic stability, moment exponential stability, Lyapunov exponent. 2000 Mathematics subject classification, Primary 60H10, Secondary 60G51, 93D20, 93D05
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