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Asymptotic properties of supercritical branching processes I: The Galton-Watson process

Published online by Cambridge University Press:  01 July 2016

N. H. Bingham  and
R. A. Doney
N. H. Bingham
Affiliation:
Westfield College, University of London
R. A. Doney
Affiliation:
University of Manchester
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Abstract

We obtain results connecting the distributions of the random variables Z1 and W in the supercritical Galton-Watson process. For example, if a > 1, and converge or diverge together, and regular variation of the tail of one of Z1, W with non-integer exponent α > 1 is equivalent to regular variation of the tail of the other.

Keywords

GALTON-WATSON PROCESSSUPERCRITICALMOMENTSTAIL-BEHAVIOURREGULAR VARIATIONLAPLACE-STIELTJES TRANSFORMFUNCTIONAL EQUATION
Type
Research Article
Information
Advances in Applied Probability , Volume 6 , Issue 4 , December 1974 , pp. 711 - 731
Copyright
Copyright © Applied Probability Trust 1974 

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