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Rates of Growth in a Class of Homogeneous Multidimensional Markov Chains

Part of: Markov processes

Published online by Cambridge University Press:  14 July 2016

M. González ,
R. Martínez  and
M. Mota
M. González*
Affiliation:
Universidad de Extremadura
R. Martínez*
Affiliation:
Universidad de Extremadura
M. Mota*
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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We investigate the asymptotic behaviour of homogeneous multidimensional Markov chains whose states have nonnegative integer components. We obtain growth rates for these models in a situation similar to the near-critical case for branching processes, provided that they converge to infinity with positive probability. Finally, the general theoretical results are applied to a class of controlled multitype branching process in which random control is allowed.

Keywords

Homogeneous multidimensional Markov chainrate of 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.)

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 43 , Issue 1 , March 2006 , pp. 159 - 174
Copyright
© Applied Probability Trust 2006 

Footnotes

Supported by the Ministerio de Ciencia y Tecnología and the FEDER through the Plan Nacional de Investigación Científica, Desarrollo e Innovación Tecnológica, grant BFM2003-06074.

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