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Some Contributions to the Theory of Near-Critical Bisexual Branching Processes

Part of: Markov processes

Published online by Cambridge University Press:  14 July 2016

M. Molina ,
M. Mota  and
A. Ramos
M. Molina*
Affiliation:
University of Extremadura
M. Mota*
Affiliation:
University of Extremadura
A. Ramos*
Affiliation:
University of Extremadura
*
∗ Postal address: Department of Mathematics, University of Extremadura, 06071 Badajoz, Spain.
∗ Postal address: Department of Mathematics, University of Extremadura, 06071 Badajoz, Spain.
∗ Postal address: Department of Mathematics, University of Extremadura, 06071 Badajoz, Spain.
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Abstract

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We investigate the probabilistic evolution of a near-critical bisexual branching process with mating depending on the number of couples in the population. We determine sufficient conditions which guarantee either the almost sure extinction of such a process or its survival with positive probability. We also establish some limiting results concerning the sequences of couples, females, and males, suitably normalized. In particular, gamma, normal, and degenerate distributions are proved to be limit laws. The results also hold for bisexual Bienaymé–Galton–Watson processes, and can be adapted to other classes of near-critical bisexual branching processes.

Keywords

Bisexual processbranching processlimiting behaviour

MSC classification

Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Type
Research Article
Information
Journal of Applied Probability , Volume 44 , Issue 2 , June 2007 , pp. 492 - 505
Copyright
Copyright © Applied Probability Trust 2007 

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