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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

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