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.
MetadatenVerfasserangaben: | Michael Hoegele, Ilya Pavlyukevich |
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DOI: | https://doi.org/10.1080/07362994.2014.858554 |
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ISSN: | 0736-2994 |
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ISSN: | 1532-9356 |
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Titel des übergeordneten Werks (Englisch): | Stochastic analysis and applications |
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Verlag: | Taylor & Francis Group |
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Verlagsort: | Philadelphia |
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Publikationstyp: | Wissenschaftlicher Artikel |
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Sprache: | Englisch |
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Jahr der Erstveröffentlichung: | 2014 |
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Erscheinungsjahr: | 2014 |
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Datum der Freischaltung: | 27.03.2017 |
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Freies Schlagwort / 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 |
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Band: | 32 |
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Ausgabe: | 1 |
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Seitenanzahl: | 28 |
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Erste Seite: | 163 |
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Letzte Seite: | 190 |
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Organisationseinheiten: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
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Peer Review: | Referiert |
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