Spectral analysis of diffusions with jump boundary

Autor(en): Kolb, Martin
Wuebker, Achim
Stichwörter: BROWNIAN-MOTION; Diffusion processes; Elliptic second-order operator; Mathematics; Non-local boundary conditions; Spectral gap
Erscheinungsdatum: 2011
Herausgeber: ACADEMIC PRESS INC ELSEVIER SCIENCE
Journal: JOURNAL OF FUNCTIONAL ANALYSIS
Volumen: 261
Ausgabe: 7
Startseite: 1992
Seitenende: 2012
Zusammenfassung: 
In this paper we consider one-dimensional diffusions with constant coefficients in a finite interval with jump boundary and a certain deterministic jump distribution. We use coupling methods in order to identify the spectral gap in the case of a large drift and prove that there is a threshold drift above which the bottom of the spectrum no longer depends on the drift. As a corollary to our result we are able to answer two questions concerning elliptic eigenvalue problems with non-local boundary conditions formulated previously by Iddo Ben-Ani and Ross Pinsky. (C) 2011 Elsevier Inc. All rights reserved.
ISSN: 00221236
DOI: 10.1016/j.jfa.2011.05.025

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