Right inverses of Lévy processes

Ron Doney, Mladen Savov

Published 2009-04-30, updated 2010-10-21Version 2

We call a right-continuous increasing process $K_x$ a partial right inverse (PRI) of a given L\'{e}vy process $X$ if $X_{K_x}=x$ for at least all $x$ in some random interval $[0,\zeta)$ of positive length. In this paper, we give a necessary and sufficient condition for the existence of a PRI in terms of the L\'{e}vy triplet.