Journal
JOURNAL OF APPLIED PROBABILITY
Volume 46, Issue 4, Pages 1116-1129Publisher
CAMBRIDGE UNIV PRESS
DOI: 10.1239/jap/1261670692
Keywords
Stochastic differential equation; Levy noise; Poisson random measure; Brownian motion; almost-sure asymptotic stability; moment exponential stability; Lyapunov exponent
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Using key tools such as Ito's formula for general semimartingales, Kunita's moment estimates for Levy-type stochastic integrals, and the exponential martingale inequality, we find conditions under which the solutions to the stochastic differential equations (SDEs) driven by Levy noise are stable in probability, almost surely and moment exponentially stable.
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