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Convolution equivalence and infinite divisibility. (English) Zbl 1051.60019
Summary: Known results relating the tail behaviour of a compound Poisson distribution function to that of its Lévy measure when one of them is convolution equivalent are extended to general infinitely divisible distributions. A tail equivalence result is obtained for random sum distributions in which the summands have a two-sided distribution.

##### MSC:
 60E07 Infinitely divisible distributions; stable distributions 60F99 Limit theorems in probability theory
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##### References:
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