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On the geometric growth in controlled branching processes with random control function

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

The limit behaviour of a controlled branching process with random control function is investigated. A necessary condition and a sufficient condition for the geometric growth of such a process are established by considering the L1-convergence. Finally, taking into account the classical X log+X criterion in branching processes, a necessary and sufficient condition is provided.

Keywords

Controlled branching processlimit theoremL1-convergence

MSC classification

Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Type
Research Papers
Information
Journal of Applied Probability , Volume 40 , Issue 4 , September 2003 , pp. 995 - 1006
Copyright
Copyright © Applied Probability Trust 2003 

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