Convolution equivalence and infinite divisibility. (English) Zbl 1051.60019

Pakes, Anthony G.

J. Appl. Probab. 41, No. 2, 407-424 (2004).

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

Keywords:

subexponential distribution; convolution equivalence; infinite divisibility; random sum; tail equivalence

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