Spectral analysis of diffusions with jump boundary

Journal article

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. © 2011 Elsevier Inc.

Authors: Kolb, M; Wübker, A

• Journal: Journal of Functional Analysis
• Volume: 261
• Issue: 7
• Pages: 1992-2012
• Publication date: 2011-10-01
• DOI: 10.1016/j.jfa.2011.05.025
• EISSN: 1096-0783
• ISSN: 0022-1236
• Language: English
• Keywords: Diffusion processes; Spectral gap; Elliptic second-order operator; Non-local boundary conditions