The closure of the convolution equivalent distribution class under convolution roots with applications to random sums

Changjun Yu, Yuebao Wang and Yang Yang

Statistics & Probability Letters, 2010, vol. 80, issue 5-6, 462-472

Abstract: Let F be a proper distribution on D=[0,[infinity]) or (-[infinity],[infinity]) and N be a non-negative integer-valued random variable with masses . Denote . The main result of this paper is that under some suitable conditions, G belongs to the convolution equivalent distribution class if and only if F belongs to the convolution equivalent distribution class. As applications, some known results on random sums have been extended and improved, which give a positive answer under certain conditions to Problem 1 of Watanabe (2008). Similarly, some corresponding results for the local distributions and densities have been obtained.

Date: 2010
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