Infinitely Divisible Distributions as Limits

Abstract

Recall that an infinitely divisible distribution is one that, for each n, is equal to Q n *n for some distribution Q n . In preceding chapters several infinitely divisible distributions have appeared. In particular all the stable distributions are infinitely divisible, as is easily seen by comparing the definitions of these two concepts. In this chapter we characterize all infinitely divisible characteristic functions. This characterization is based on the family of ‘compound Poisson distributions’, to be introduced in the first section.