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On the class of controlled branching processes with random control functions

Part of: Markov processes

Published online by Cambridge University Press:  14 July 2016

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

In this paper, the class of controlled branching processes with random control functions introduced by Yanev (1976) is considered. For this class, necessary and sufficient conditions are established for the process to become extinct with probability 1 and the limit probabilistic behaviour of the population size, suitably normed, is investigated.

Keywords

Controlled branching processesextinction probabilitylimit theorems

MSC classification

Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Type
Research Papers
Information
Journal of Applied Probability , Volume 39 , Issue 4 , December 2002 , pp. 804 - 815
Copyright
Copyright © Applied Probability Trust 2002 

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Footnotes

Research supported by the Plan Nacional de Investigación Cientifíca, Desarrollo e Innovación Tecnológica, grant BFM 2000-0356.

References

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