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On the geometric growth in a class of homogeneous multitype Markov chain

Part of: Markov processes

Published online by Cambridge University Press:  14 July 2016

M. González ,
R. Martínez  and
M. Mota
M. González*
Affiliation:
University of Extremadura
R. Martínez*
Affiliation:
University of Extremadura
M. Mota*
Affiliation:
University of Extremadura
*
∗Postal address: Departamento de Matemáticas, Facultad de Ciencias, Avda. Elvas s/n, 06071 Badajoz, Spain.
∗Postal address: Departamento de Matemáticas, Facultad de Ciencias, Avda. Elvas s/n, 06071 Badajoz, Spain.
∗Postal address: Departamento de Matemáticas, Facultad de Ciencias, Avda. Elvas s/n, 06071 Badajoz, Spain.
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Abstract

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In this paper, we investigate the geometric growth of homogeneous multitype Markov chains whose states have nonnegative integer coordinates. Such models are considered in a situation similar to the supercritical case for branching processes. Finally, our general theoretical results are applied to a class of controlled multitype branching process in which the control is random.

Keywords

Homogeneous multitype Markov chaingeometric growthmultitype branching process

MSC classification

Primary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)
Secondary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Type
Research Papers
Information
Journal of Applied Probability , Volume 42 , Issue 4 , December 2005 , pp. 1015 - 1030
Copyright
© Applied Probability Trust 2005 

References

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