Right inverses of Lévy processes

Ron Doney; Mladen Savov

doi:10.1214/09-AOP515

paper

Right inverses of Lévy processes

arXiv:0904.4871 · doi:10.1214/09-AOP515

Abstract

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

Published in at http://dx.doi.org/10.1214/09-AOP515 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)