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.

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Metadaten
Author details:Markus KleinGND, Pierre-André Zitt
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):License LogoKeine öffentliche Lizenz: Unter Urheberrechtsschutz
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