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A note on extinction criteria for bisexual Galton-Watson processes

Published online by Cambridge University Press:  14 July 2016

F. Thomas Bruss
F. Thomas Bruss*
Affiliation:
Facultés Universitaires Notre-Dame de la Paix, Namur
*
∗Postal address: Département de Mathématique, FNDP, Rempart de la Vierge 8, B-5000 Namur, Belgium.
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Abstract

This note deals with extinction criteria for bisexual Galton–Watson processes with arbitrary mating functions in terms of the averaged reproduction mean per mating unit. It gives a satisfactory answer to a question put forward by Hull (1982).

Keywords

GENERAL BISEXUAL MATING FUNCTIONSPHI-BRANCHING PROCESSESABSORBING PROCESSES
Type
Short Communications
Information
Journal of Applied Probability , Volume 21 , Issue 4 , December 1984 , pp. 915 - 919
Copyright
Copyright © Applied Probability Trust 1984 

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References

Daley, D. J. (1968) Extinction conditions for certain bisexual Galton–Watson branching processes. Z. Wahrscheinlichkeitsth. 9, 315–322.CrossRefGoogle Scholar
Hull, D. M. (1982) A necessary condition for extinction in those bisexual Galton–Watson branching processes governed by superadditive mating functions. J. Appl. Prob. 19, 847–850.CrossRefGoogle Scholar
Sevastyanov, B. A. and Zubkov, A. M. (1974) Controlled branching processes. Theory Prob. Appl. 19, 14–24.Google Scholar