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The Galton-Watson process with mean one

Published online by Cambridge University Press:  14 July 2016

E. Seneta
E. Seneta*
Affiliation:
Australian National University
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Extract

Let Zn be the number of individuals in the n-th generation of a simple (discrete, one-type) Galton-Watson process, descended from a single ancestor. Write and assume, as usual, that 0 < F(0) < 1. It is well known that the p.g.f. of Zn is Fn(s), the n-th functional iterate of F(s), and that if the process is construed as a Markov chain on the states 0, 1, 2,…, then its n-step transition probabilities are given by

Type
Research Papers
Information
Journal of Applied Probability , Volume 4 , Issue 3 , November 1967 , pp. 489 - 495
Copyright
Copyright © Applied Probability Trust 

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References

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