Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-28T04:53:58.839Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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