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Convolution equivalence and infinite divisibility

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: School 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

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.

Keywords

Subexponential distributionconvolution equivalenceinfinite divisibilityrandom sumtail equivalence

MSC classification

Primary: 60E07: Infinitely divisible distributions; stable distributions 60F99: None of the above, but in this section
Type
Research Papers
Information
Journal of Applied Probability , Volume 41 , Issue 2 , June 2004 , pp. 407 - 424
Copyright
Copyright © Applied Probability Trust 2004 

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