As remarked by van Harn & Steutel, infinite divisibility of probability measures μ1 on dR + can be characterized as a kind of self-decomposability of μ with respect to the exponential family generated by μ, and we shall here give similar characterizations of certain classes of infinitely divisible probabilities on dR +, in particular the generalized Γ-convolutions and the usual self-decomposable probability measures.
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Berg et al. (1982) studied this question.
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