On multivariate infinitely divisible distributions

R.A. Horn, F.W. Steutel

Research output: Contribution to journalArticleAcademicpeer-review

10 Citations (Scopus)


Simple conditions are given which characterize the generating function of a nonnegative multivariate infinitely divisible random vector. Necessary conditions on marginals, linear combinations, tail behavior, and zeroes are discussed, and a sufficient condition is given. The latter condition, which is a multivariate generalization of ordinary log-convexity, is shown to characterize only certain products of univariate infinitely divisible distributions.
Original languageEnglish
Pages (from-to)139-151
Number of pages13
JournalStochastic Processes and their Applications
Issue number2
Publication statusPublished - 1978


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