a Department of Statistics, Oxford University, 1 South Parks Road, Oxford, OX1 3TG, UK b Fachbereich Mathematik, Universität Osnabrück, Albrechtstrasse 28a, 49076 Osnabrück, Germany
Abstract:
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-Ari and Ross Pinsky.