On Series Representations of Infinitely Divisible Random Vectors

Abstract

General results on series representations, involving arrival times in a Poisson process, are established for infinitely divisible Banach space valued random vectors without Gaussian components. Applying these results, various generalizations of LePage's representation are obtained in a unified way. Certain conditionally Gaussian infinitely divisible random vectors are characterized and some problems related to a Gaussian randomization method are investigated.