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On the limit behaviour of a superadditive bisexual Galton–Watson branching process

Part of: Markov processes

Published online by Cambridge University Press:  14 July 2016

M. Gonzalez  and
M. Molina
M. Gonzalez*
Affiliation:
Universidad de Extremadura
M. Molina*
Affiliation:
Universidad de Extremadura
*
∗Postal address: Departamento de Matemáticas, Fac. de Ciencias, Universidad de Extremadura, 06071-Badajoz, Spain. E-mail: mvelasco@ba.unex.es
∗Postal address: Departamento de Matemáticas, Fac. de Ciencias, Universidad de Extremadura, 06071-Badajoz, Spain. E-mail: mvelasco@ba.unex.es
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Abstract

The asymptotic behaviour of a superadditive bisexual Galton–Watson branching process is studied. Sufficient conditions for the almost sure and L1 convergence of the suitably normed process are given. Finally, a first approach to the study of the L1 convergence for a superadditive bisexual Galton–Watson branching process under the Z log+Z condition is considered.

Keywords

BISEXUAL GALTON–WATSON BRANCHING PROCESSMARTINGALESALMOST SURE CONVERGENCEL1 CONVERGENCE

MSC classification

Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Type
Research Papers
Information
Journal of Applied Probability , Volume 33 , Issue 4 , December 1996 , pp. 960 - 967
Copyright
Copyright © Applied Probability Trust 1996 

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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
Bruss, F. T. (1984) A note on extinction criteria for bisexual Galton-Watson branching processes. J. Appl. Prob. 21, 915–919.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
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.Google Scholar
Hull, D. M. (1984) Conditions for extinction in certain bisexual Galton-Watson branching processes. J. Appl. Prob. 21, 414–418.CrossRefGoogle Scholar
Klebaner, F. C. (1984) Geometric rate of growth in population-size-dependent branching processes. J. Appl. Prob. 21, 40–49.Google Scholar
Klebaner, F. C. (1985) A limit theorem for population-size-dependent branching processes. J. Appl. Prob. 22, 48–57.Google Scholar