A condition for absolute continuity of infinitely divisible distribution functions

Abstract

Throughout this paper the symbols r.v., d.f., ch.f., and i.d. will stand, respectively, for "random variable", "distribution function", "characteristic function", and "infinitely divisible". Let F(x) be an i.d.d.f. Hartman and Wintner [5] and Blum and Rosenblatt [1] have given a condition, necessary and sufficient, for F(x) to be a continuous d.f. In this note a sufficient condition for F(x) to be an absolutely continuous d.f. is given. © 1963 Springer-Verlag.