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Asymptotic properties of super-critical branching processes II: Crump-Mode and Jirina processes

Published online by Cambridge University Press:  01 July 2016

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

We obtain results connecting the distribution of the random variables Y and W in the supercritical generalized branching processes introduced by Crump and Mode. For example, if β > 1, EYβ and EWβ converge or diverge together and regular variation of the tail of one of Y, W with non-integer exponent β > 1 is equivalent to regular variation of the other. We also prove analogous results for the continuous-time continuous state-space branching processes introduced by Jirina.

Keywords

GENERAL BRANCHING PROCESSSUPERCRITICALMOMENTSTAIL BEHAVIOURREGULAR VARIATIONLAPLACE-STIELTJES TRANSFORM
Type
Research Article
Information
Advances in Applied Probability , Volume 7 , Issue 1 , March 1975 , pp. 66 - 82
Copyright
Copyright © Applied Probability Trust 1975 

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References

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