On maximum family size in branching processes

Ibrahim Rahimov; George P. Yanev

doi:10.1239/jap/1032374622

On maximum family size in branching processes

Ibrahim Rahimov, George P. Yanev^*

^*Corresponding author for this work

King Fahd University of Petroleum & Minerals

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

The number Yn of offspring of the most prolific individual in the nth generation of a Bienaymé-Galton-Watson process is studied. The asymptotic behaviour of Y_n as n → ∞ may be viewed as an extreme value problem for i.i.d. random variables with random sample size. Limit theorems for both Y_n and EY_n provided that the offspring mean is finite are obtained using some convergence results for branching processes as well as a transfer limit lemma for maxima. Subcritical, critical and supercritical branching processes are considered separately.

Original language	English
Pages (from-to)	632-643
Number of pages	12
Journal	Journal of Applied Probability
Volume	36
Issue number	3
DOIs	https://doi.org/10.1239/jap/1032374622
State	Published - 1999

Keywords

Bienaymé-Galton-Watson branching process
Max-semi-stability
Max-stability
Random sample size
Transfer theorems

ASJC Scopus subject areas

Statistics and Probability
General Mathematics
Statistics, Probability and Uncertainty

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10.1239/jap/1032374622

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AU - Yanev, George P.

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AB - The number Yn of offspring of the most prolific individual in the nth generation of a Bienaymé-Galton-Watson process is studied. The asymptotic behaviour of Yn as n → ∞ may be viewed as an extreme value problem for i.i.d. random variables with random sample size. Limit theorems for both Yn and EYn provided that the offspring mean is finite are obtained using some convergence results for branching processes as well as a transfer limit lemma for maxima. Subcritical, critical and supercritical branching processes are considered separately.

KW - Bienaymé-Galton-Watson branching process

KW - Max-semi-stability

KW - Max-stability

KW - Random sample size

KW - Transfer theorems

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EP - 643

JO - Journal of Applied Probability

JF - Journal of Applied Probability

IS - 3

ER -

On maximum family size in branching processes

Abstract

Keywords

ASJC Scopus subject areas

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