Stability of stochastic differential equations with Lévy noise

2014 ◽  
Author(s):  
Quanxin Zhu
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Lévy Noise ◽  
Levy Noise

scholarly journals Asymptotic Stability of Stochastic Differential Equations Driven by Lévy Noise

2009 ◽  
Vol 46 (4) ◽  
pp. 1116-1129 ◽  
Author(s):  
David Applebaum ◽  
Michailina Siakalli
Keyword(s):  
Asymptotic Stability ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Lévy Noise ◽  
Stochastic Integrals ◽  
Martingale Inequality ◽  
Moment Estimates ◽  
Exponential Martingale ◽  
Exponentially Stable ◽  
Levy Noise

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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