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On the L2-convergence of a superadditive bisexual Galton-Watson branching process

Part of: Markov processes

Published online by Cambridge University Press:  14 July 2016

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

In this paper the L2-convergence of a superadditive bisexual Galton–Watson branching process is studied. Necessary and sufficient conditions for the convergence of the suitably normed process are given. In the final section, a result about one of the most important bisexual models is proved.

Keywords

BISEXUAL GALTON–WATSON BRANCHING PROCESSL2-CONVERGENCE

MSC classification

Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Type
Research Papers
Information
Journal of Applied Probability , Volume 34 , Issue 3 , September 1997 , pp. 575 - 582
Copyright
Copyright © Applied Probability Trust 1997 

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References

Bagley, J. H. (1986) On the asymptotic properties of a supercritical bisexual branching process. J. Appl. Prob. 23, 820–826.Google Scholar
Daley, D. J. (1968) Extinction condition for certain bisexual Galton-Watson branching processes. Z. Wahrscheinlichkeitsth. 9, 315–322.CrossRefGoogle Scholar
Daley, D. J., Hull, D. M. and Taylor, J. M. (1986) Bisexual Galton-Watson branching processes with superadditive mating functions. J. Appl. Prob. 23, 585–600.Google Scholar
González, M. and Molina, M. (1996) On the limit behaviour of a superadditive bisexual Galton-Watson branching process. J. Appl. Prob 33, 960–967.CrossRefGoogle Scholar
Hille, E. and Phillips, R. S. (1957) Functional Analysis and Semi-Groups (Amer. Math. Soc. Colloq. XXXI). AMS, Providence, RI.Google Scholar
Klebaner, F. C. (1984) Geometric rate of growth in population-size-dependent branching processes. J. Appl. Prob. 21, 40–49.CrossRefGoogle Scholar