Maller, Ross2021-04-142021-04-140040-585Xhttp://hdl.handle.net/1885/229850We 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.This research was partially supported by ARC grant DP1092502application/pdfen-AU© 2018 Society for Industrial and Applied Mathematicsregularity of a real-valued L´evy processdominance of the positive part of a L´evy process over the negative partfirst passage of a L´evy process below zerofirst passage timedominated variation conditionsRogozin regularity condition2018-08-0810.1137/S0040585X97T9888242020-11-23