On the Spectral Gap of Brownian Motion with Jump Boundary

Details On the Spectral Gap of Brownian Motion with Jump Boundary On the Spectral Gap of Brownian Motion with Jump Boundary

2011-01-18

arxiv.org/abs/1101.3556v1

Mathematics

Probability

18 pages

Scientific paper

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 on the jump distribution in a multi-dimensional setting.

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