Spectral analysis of diffusions with jump boundary

Kolb, M. and Wübker, A. (2011) Spectral analysis of diffusions with jump boundary. Journal of Functional Analysis, 261 (7). pp. 1992-2012. ISSN 0022-1236 doi: 10.1016/j.jfa.2011.05.025

Abstract/Summary

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.