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An age dependent branching process with variable lifetime distribution: The generation size

Published online by Cambridge University Press:  01 July 2016

Robert Fildes
Robert Fildes*
Affiliation:
Manchester Business School
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Abstract

In a branching process with variable lifetime, introduced by Fildes (1972) define Yjk(t) as the number of particles alive in generation k at time t when the initial particle is born in generation j. A limit law similar to that derived in the Bellman-Harris process is proved where it is shown that Yjk(t) suitably normalised converges in mean square to a random variable which is the limit random variable of Znm–n in the Galton-Watson process (m is the mean number of particles born).

Keywords

AGE-DEPENDENTBRANCHING PROCESSMULTI-TYPEVARIABLE LIFETIMEGENERATIONBELLMAN-HARRIS
Type
Research Article
Information
Advances in Applied Probability , Volume 6 , Issue 2 , June 1974 , pp. 291 - 308
Copyright
Copyright © Applied Probability Trust 1974 

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References

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