On the spectral gap of Brownian motion with jump boundary

Autor(en): Kolb, Martin
Wuebker, Achim
Stichwörter: Brownian motion, coupling; jump-boundary; jump-process; Mathematics; spectral gap; spectral gap property; speed of convergence; Statistics & Probability
Erscheinungsdatum: 2011
Herausgeber: UNIV WASHINGTON, DEPT MATHEMATICS
Journal: ELECTRONIC JOURNAL OF PROBABILITY
Volumen: 16
Startseite: 1214
Seitenende: 1237
Zusammenfassung: 
In this paper we consider the Brownian motion with jump boundary and present a new proof of a recent result of Li, Leung and Rakesh concerning the exact convergence rate in the one-dimensional case. Our methods are different and mainly probabilistic relying on coupling methods adapted to the special situation under investigation. Moreover we answer a question raised by Ben-Ari and Pinsky concerning the dependence of the spectral gap from the jump distribution in a multi-dimensional setting.
ISSN: 10836489
DOI: 10.1214/EJP.v16-903

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