Articlebronze2009

Asymptotic Stability of Stochastic Differential Equations Driven by Lévy Noise

134 citations0/0 files storedJournal of Applied Probability

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Stochastic processes and financial applications Stability and Control of Uncertain Systems Nonlinear Differential Equations Analysis

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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References

2003Financial Modelling with Jump Processes 2004Lévy Processes and Stochastic Calculus 2009Lévy Processes and Stochastic Calculus 1997Stochastic differential equations and their applications 2005Applied Stochastic Control of Jump Diffusions 2001Lévy-Driven Carma Processes 2004Stochastic Differential Equations Based on Lévy Processes and Stochastic Flows of Diffeomorphisms

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