| | |
Summary: Stochastic Stabilization of Dynamical Systems using 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, michailina27@gmail.com
Abstract
We investigate the perturbation of the non-linear differential equation dx(t)
dt =
f(x(t)) by random noise terms consisting of Brownian motion and an independent
Poisson random measure. We find conditions under which the perturbed system
is almost surely exponentially stable and estimate the corresponding Lyapunov
exponents.
Keywords: stochastic differential equation, L´evy noise, Poisson random measure,
Brownian motion, L´evy process, CGMY process, almost sure asymptotic stability,
Lyapunov exponent, stabilization, destabilization
2000 Mathematics subject classification, Primary 93E15, Secondary 60H10,
60G51, 93D20
|
