On the spectral gap of Brownian motion with jump boundary

Kolb, M. and Wübker, A. (2011) On the spectral gap of Brownian motion with jump boundary. Electronic Journal of Probability, 16. pp. 1214-1237. ISSN 1083-6489 doi: 10.1214/EJP.v16-903

Abstract/Summary

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 dierent 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.