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Asymptotic Stability of Stochastic Differential Equations Driven by Levy Noise
 

Summary: Asymptotic Stability of Stochastic Differential Equations
Driven by L´evy Noise
David Applebaum and Michailina Siakalli
Department of Probability and Statistics,
University of Sheffield,
Hicks Building, Hounsfield Road,
Sheffield, England, S3 7RH
e-mail: D.Applebaum@sheffield.ac.uk, michaelina27@gmail.com
Abstract
Using key tools such as It^o's formula for general semimartingales, Kunita's
moment estimates for L´evy-type stochastic integrals, and the exponential
martingale inequality, we find conditions under which the solutions to the stochastic
differential equations (SDEs) driven by L´evy noise are stable in probability, almost
surely and moment exponentially stable.
Keywords; stochastic differential equation, L´evy 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
1 Introduction

  

Source: Applebaum, David - Department of Probability and Statistics, University of Sheffield

 

Collections: Mathematics