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Weak convergence of the simple birth-and-death process

Published online by Cambridge University Press:  14 July 2016

Constantin Ivan
Constantin Ivan*
Affiliation:
University of Duisburg
*
∗Postal address: Gesamthochschule Duisburg, Fachbereich 11, Postfach 10 16 29, 4100 Duisburg 1, W. Germany.
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Abstract

The existence of a weak limit birth-and-death process on the natural integers for the simple birth-and-death process conditional on non-extinction up to time t as t→∞ is proved. Starting from the latter a new weak limiting procedure yields a diffusion Markov process on the positive infinite semi-axis.

Keywords

SIMPLE BIRTH-AND-DEATH PROCESSESWEAK CONVERGENCE
Type
Short Communications
Information
Journal of Applied Probability , Volume 18 , Issue 1 , March 1981 , pp. 245 - 252
Copyright
Copyright © Applied Probability Trust 

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References

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