Extensions of Regularity for a Levy Process

Abstract

We obtain necessary and sufficient conditions for the finiteness of certain moment functions of the random variable T0(-), which is the first passage time of a Levy process (X-t)(t >= 0) below zero, and the position XT0- of the process at this time. Our results generalize classical results of Rogozin and Bertoin on the regularity of X, and extend earlier results of Blumenthal and Getoor on the regularity index.