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Asymptotic behaviour of Markov population processes by asymptotically linear rate of change

Part of: Markov processes

Published online by Cambridge University Press:  14 July 2016

F. C. Klebaner
F. C. Klebaner*
Affiliation:
University of Melbourne
*
∗ Postal address: Department of Statistics, Richard Berry Building, University of Melbourne, Parkville, VIC 3052, Australia.
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Abstract

Multidimensional Markov processes in continuous time with asymptotically linear mean change per unit of time are studied as randomly perturbed linear differential equations. Conditions for exponential and polynomial growth rates with stable type distribution are given. From these conditions results on branching models of populations with stabilizing reproduction for near-supercritical and near-critical cases follow.

Keywords

MULTITYPE POPULATIONLINEAR DIFFERENTIAL EQUATIONSMULTIDIMENSIONAL MARKOV PROCESS

MSC classification

Primary: 60J27: Continuous-time Markov processes on discrete state spaces
Type
Research Papers
Information
Journal of Applied Probability , Volume 31 , Issue 3 , September 1994 , pp. 614 - 625
Copyright
Copyright © Applied Probability Trust 1994 

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Footnotes

Research supported by the Australian Research Council grant A68930440.

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