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Convolution Equivalence and Infinite Divisibility: Corrections and Corollaries

Part of: Limit theorems Distribution theory - Probability

Published online by Cambridge University Press:  14 July 2016

Anthony G. Pakes
Anthony G. Pakes*
Affiliation:
University of Western Australia
*
∗ Postal address: Department of Mathematics and Statistics, University of Western Australia, 35 Stirling Highway, Crawley, WA 6009, Australia. Email address: pakes@maths.uwa.edu.au
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Abstract

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Corrections are made to formulations and proofs of some theorems about convolution equivalence closure for random sum distributions. These arise because of the falsity of a much used asymptotic equivalence lemma, and they impinge on the convolution equivalence closure theorem for general infinitely divisible laws.

Keywords

Subexponential distributionsconvolution equivalenceinfinite divisibilityrandom sumstail equivalence

MSC classification

Primary: 60E07: Infinitely divisible distributions; stable distributions 60F99: None of the above, but in this section
Type
Research Article
Information
Journal of Applied Probability , Volume 44 , Issue 2 , June 2007 , pp. 295 - 305
Copyright
Copyright © Applied Probability Trust 2007 

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