Resonances for a diffusion with small noise
- We study resonances for the generator of a diffusion with small noise in R(d) : L = -∈∆ + ∇F * ∇, when the potential F grows slowly at infinity (typically as a square root of the norm). The case when F grows fast is well known, and under suitable conditions one can show that there exists a family of exponentially small eigenvalues, related to the wells of F. We show that, for an F with a slow growth, the spectrum is R+, but we can find a family of resonances whose real parts behave as the eigenvalues of the "quick growth" case, and whose imaginary parts are small.
Author details: | Markus KleinGND, Pierre-André Zitt |
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URN: | urn:nbn:de:kobv:517-opus-49448 |
Publication series (Volume number): | Mathematische Statistik und Wahrscheinlichkeitstheorie : Preprint (2008, 02) |
Publication type: | Preprint |
Language: | English |
Publication year: | 2008 |
Publishing institution: | Universität Potsdam |
Release date: | 2011/03/30 |
RVK - Regensburg classification: | SI 990 |
Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
DDC classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
License (German): | Keine öffentliche Lizenz: Unter Urheberrechtsschutz |