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The asymptotic behaviour of birth and death and some related processes

Published online by Cambridge University Press:  01 July 2016

Andrew D. Barbour
Andrew D. Barbour*
Affiliation:
University of Cambridge
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Abstract

The paper examines those continuous time Markov processes Z(·) on the positive integers which have the ‘skip free upwards’ property, with regard to their asymptotic behaviour in the event of Z(t) tending to infinity. The behaviour is characterised in terms of the convergence or divergence of an appropriate function of Z(t), and the description is improved by central limit and iterated logarithm theorems. The conditions of the theorems are expressed entirely in terms of the matrix Q of instantaneous transition rates for Z(·). The method is applied, by way of example, to the super-critical linear birth and death process.

Keywords

BIRTH AND DEATHCENTRAL LIMITITERATED LOGARITHM
Type
Research Article
Information
Advances in Applied Probability , Volume 7 , Issue 1 , March 1975 , pp. 28 - 43
Copyright
Copyright © Applied Probability Trust 1975 

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