Asymptotic stability of stochastic differential equations driven by Lévy noise

Asymptotic stability of stochastic differential equations driven by Lévy noise

David Applebaum and Michailina Siakalli

Source: J. Appl. Probab. Volume 46, Number 4 (2009), 1116-1129.

Abstract

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.

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Primary Subjects: 60H10

Secondary Subjects: 60G51, 93D20, 93D05

Keywords: Stochastic differential equation; Lévy noise; Poisson random measure; Brownian motion; almost-sure asymptotic stability; moment exponential stability; Lyapunov exponent

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Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.jap/1261670692
Digital Object Identifier: doi:10.1239/jap/1261670692
Mathematical Reviews number (MathSciNet): MR2582710

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