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On the maximal offspring in a critical branching process with infinite mean


Bertoin, J (2011). On the maximal offspring in a critical branching process with infinite mean. Journal of Applied Probability, 48(2):576-582.

Abstract

We investigate the maximal number Mk of offspring amongst all individuals in a critical Galton-Watson process started with k ancestors. We show that when the reproduction law has a regularly varying tail with index -α for 1 < α < 2, then k-1Mk converges in distribution to a Frechet law with shape parameter 1 and scale parameter depending only on α.

Abstract

We investigate the maximal number Mk of offspring amongst all individuals in a critical Galton-Watson process started with k ancestors. We show that when the reproduction law has a regularly varying tail with index -α for 1 < α < 2, then k-1Mk converges in distribution to a Frechet law with shape parameter 1 and scale parameter depending only on α.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:2011
Deposited On:24 Apr 2013 14:32
Last Modified:07 Dec 2017 20:55
Publisher:Applied Probability Trust
ISSN:0021-9002
Publisher DOI:https://doi.org/10.1239/jap/1308662646

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