Journal of Applied Probability

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

Jean Bertoin

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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.

Article information

Source
J. Appl. Probab., Volume 48, Number 2 (2011), 576-582.

Dates
First available in Project Euclid: 21 June 2011

Permanent link to this document
https://projecteuclid.org/euclid.jap/1308662646

Digital Object Identifier
doi:10.1239/jap/1308662646

Mathematical Reviews number (MathSciNet)
MR2840318

Zentralblatt MATH identifier
1223.60020

Subjects
Primary: 60F05: Central limit and other weak theorems 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)

Keywords
Branching process maximal offspring Frechet distribution stable Lévy process extreme value theory

Citation

Bertoin, Jean. On the maximal offspring in a critical branching process with infinite variance. J. Appl. Probab. 48 (2011), no. 2, 576--582. doi:10.1239/jap/1308662646. https://projecteuclid.org/euclid.jap/1308662646


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References

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