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Bisexual Galton-Watson branching process with population-size-dependent mating

Part of: Markov processes

Published online by Cambridge University Press:  14 July 2016

M. Molina ,
M. Mota  and
A. Ramos
M. Molina*
Affiliation:
Universidad de Extremadura
M. Mota*
Affiliation:
Universidad de Extremadura
A. Ramos*
Affiliation:
Universidad de Extremadura
*
∗ Postal address: Departamento de Matemáticas, Facultad de Ciencias, 06071 Badajoz, Spain.
∗ Postal address: Departamento de Matemáticas, Facultad de Ciencias, 06071 Badajoz, Spain.
∗ Postal address: Departamento de Matemáticas, Facultad de Ciencias, 06071 Badajoz, Spain.
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Abstract

In this paper, we introduce a bisexual Galton-Watson branching process with mating function dependent on the population size in each generation. Necessary and sufficient conditions for the process to become extinct with probability 1 are investigated for two possible conditions on the sequence of mating functions. Some results for the probability generating functions associated with the process are also given.

Keywords

Bisexual Galton-Watson branching processespopulation-size-dependent branching processesextinction probability

MSC classification

Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Type
Research Papers
Information
Journal of Applied Probability , Volume 39 , Issue 3 , September 2002 , pp. 479 - 490
Copyright
Copyright © Applied Probability Trust 2002 

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Footnotes

Research supported by the Plan Nacional de Investigación Cientifíca, Desarrollo e Innovación Tecnológica, grant BFM2000-0356.

References

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