The exit problem from a neighborhood of the global attractor for dynamical systems perturbed by heavy-tailed levy processes
- 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.
Author details: | Michael Hoegele, Ilya Pavlyukevich |
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DOI: | https://doi.org/10.1080/07362994.2014.858554 |
ISSN: | 0736-2994 |
ISSN: | 1532-9356 |
Title of parent work (English): | Stochastic analysis and applications |
Publisher: | Taylor & Francis Group |
Place of publishing: | Philadelphia |
Publication type: | Article |
Language: | English |
Year of first publication: | 2014 |
Publication year: | 2014 |
Release date: | 2017/03/27 |
Tag: | Canonical (Marcus) SDE; First exit location; First exit time; Global attractor; Ito SDE; Multiplicative noise; Regular variation; Stratonovich SDE; Van der Pol oscillator; alpha-stable Levy process |
Volume: | 32 |
Issue: | 1 |
Number of pages: | 28 |
First page: | 163 |
Last Page: | 190 |
Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
Peer review: | Referiert |