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Asymptotic behaviour of critical controlled branching processes with random control functions

Published online by Cambridge University Press:  14 July 2016

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, Universidad de Extremadura, 06071 Badajoz, Spain.
Postal address: Departamento de Matemáticas, Facultad de Ciencias, Universidad de Extremadura, 06071 Badajoz, Spain.
Postal address: Departamento de Matemáticas, Facultad de Ciencias, Universidad de Extremadura, 06071 Badajoz, Spain.
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Abstract

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In this paper, we investigate the asymptotic behaviour of controlled branching processes with random control functions. In a critical case, we establish sufficient conditions for both their almost-sure extinction and for their nonextinction with a positive probability. For some suitably chosen norming constants, we also determine different kinds of limiting behaviour for this class of processes.

Type
Research Papers
Copyright
© Applied Probability Trust 2005 

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