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The asymptotic behaviour of a divergent linear birth and death process

Published online by Cambridge University Press:  14 July 2016

John Haigh
John Haigh*
Affiliation:
University of Sussex
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Abstract

A recent paper in Advances in Applied Probability (Siegel (1976)) considered the duration of the time Tmn for a linear birth and death process to grow from a (large) initial size m to a larger size n. The main aim was to show that, when the birth rate exceeds the death rate, Tmn is close to its mean value, log n/m, with high probability. This paper establishes this result using much simpler techniques.

Keywords

BIRTH AND DEATH PROCESSESASYMPTOTIC GROWTHFIRST ENTRY TIMES
Type
Short Communications
Information
Journal of Applied Probability , Volume 15 , Issue 1 , March 1978 , pp. 187 - 191
Copyright
Copyright © Applied Probability Trust 1978 

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References

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