The asymptotic behaviour of a divergent linear birth and death process
- 1 March 1978
- journal article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 15 (1) , 187-191
- https://doi.org/10.2307/3213250
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
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