Fredholm and Sturm--Liouville Type Characterizations of the Limit Measure for the Kac Killing Penalization for Lévy Processes

Abstract

We study the Kac killing penalization for a one-dimensional recurrent Lévy process. We prove that the limit process possesses two equivalent characterizations by a Fredholm equation and by a Sturm--Liouville equation.

arXiv comment35 pages