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A convergence theorem for parities in a birth-and-death process

Published online by Cambridge University Press:  14 July 2016

I. W. Saunders
I. W. Saunders*
Affiliation:
C.S.I.R.O. Division of Mathematics and Statistics, Canberra
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Abstract

The parity of an individual in a population process is the number of offspring that individual has produced. If Nk(t) is the number of individuals of parity k at time t in a birth-and-death process and we show that, conditional on N(t)→ ∞,

Keywords

BIRTH-AND-DEATH PROCESSPARITYALMOST SURE CONVERGENCE
Type
Research Papers
Information
Journal of Applied Probability , Volume 13 , Issue 2 , June 1976 , pp. 231 - 238
Copyright
Copyright © Applied Probability Trust 1976 

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References

Feller, W. (1968), (1971) An Introduction to Probability Theory and its Applications. Vol. I, 3rd edn. and Vol. II, 2nd edn. Wiley, New York.Google Scholar
Gani, J. and Saunders, I. W. (1976) On the parity of individuals in a branching process. J. Appl. Prob. 13, 219–230.CrossRefGoogle Scholar