TY  - JOUR
A1  - Hoegele, Michael
A1  - Pavlyukevich, Ilya
T1  - The exit problem from a neighborhood of the global attractor for dynamical systems perturbed by heavy-tailed levy processes
JF  - Stochastic analysis and applications
N2  - We consider a finite-dimensional deterministic dynamical system with the global attractor ? which supports a unique ergodic probability measure P. The measure P can be considered as the uniform long-term mean of the trajectories staying in a bounded domain D containing ?. We perturb the dynamical system by a multiplicative heavy tailed Levy noise of small intensity E>0 and solve the asymptotic first exit time and location problem from D in the limit of E?0. In contrast to the case of Gaussian perturbations, the exit time has an algebraic exit rate as a function of E, just as in the case when ? is a stable fixed point studied earlier in [9, 14, 19, 26]. As an example, we study the first exit problem from a neighborhood of the stable limit cycle for the Van der Pol oscillator perturbed by multiplicative -stable Levy noise.
KW  - alpha-stable Levy process
KW  - Canonical (Marcus) SDE
KW  - First exit location
KW  - First exit time
KW  - Global attractor
KW  - Ito SDE
KW  - Multiplicative noise
KW  - Regular variation
KW  - Stratonovich SDE
KW  - Van der Pol oscillator
Y1  - 2014
U6  - https://doi.org/10.1080/07362994.2014.858554
SN  - 0736-2994
SN  - 1532-9356
VL  - 32
IS  - 1
SP  - 163
EP  - 190
PB  - Taylor & Francis Group
CY  - Philadelphia
ER  -