On the decomposition of infinitely divisible characteristic functions with continuous Poisson spectrum. II

Roger Cuppens

Vol. 29 (1969), No. 3, 521–525

DOI: 10.2140/pjm.1969.29.521

Abstract

Let f be an infinitely divisible characteristic function whose spectral functions are absolutely continuous functions with almost everywhere continuous derivatives. Some necessary conditions that f belong to the class I₀ of the infinitely divisible characteristic functions without indecomposable factors have been obtained by Cramér, Shimizu and the author and a sufficient condition that f belong to I₀ has been given by Ostrovskiy. In the present work, we prove that the condition of Ostrovskiy is not only a sufficient, but also a necessary condition that f belong to I₀.

Mathematical Subject Classification

Primary: 60.20

Milestones

Received: 27 May 1968

Published: 1 June 1969