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Asymptotic Stability of Stochastic Differential Equations Driven by Lévy Noise

Part of: Stochastic processes Stochastic analysis Stability

Published online by Cambridge University Press:  14 July 2016

David Applebaum  and
Michailina Siakalli
David Applebaum*
Affiliation:
University of Sheffield
Michailina Siakalli*
Affiliation:
University of Sheffield
*
∗Postal address: Department of Probability and Statistics, University of Sheffield, Hicks Building, Hounsfield Road, Sheffield, S3 7RH, UK. Email address: d.applebaum@sheffield.ac.uk
∗∗Email address: michailina27@gmail.com
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Abstract

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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 equationLévy noisePoisson random measureBrownian motionalmost-sure asymptotic stabilitymoment exponential stabilityLyapunov exponent

MSC classification

Secondary: 60H10: Stochastic ordinary differential equations 60G51: Processes with independent increments; L'evy processes 93D20: Asymptotic stability 93D05: Lyapunov and other classical stabilities (Lagrange, Poisson, $L^p, l^p$, etc.)
Type
Research Article
Information
Journal of Applied Probability , Volume 46 , Issue 4 , December 2009 , pp. 1116 - 1129
Copyright
Copyright © Applied Probability Trust 2009 

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