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Functional equations and the Galton-Watson process

Published online by Cambridge University Press:  01 July 2016

E. Seneta*
Affiliation:
Australian National University

Extract

In the present exposition we are concerned only with the simple Galton-Watson process, initiated by a single ancestor (Harris (1963), Chapter I). Let denote the probability generating function of the offspring distribution of a single individual. Our fundamental assumption, which holds throughout the sequel, is that fj ≠ 1, j = 0,1,2, …; in particular circumstances it shall be necessary to strengthen this to 0 < f0F(0) < 1, which is the relevant assumption when extinction behaviour is to be considered. (Even so, our assumptions will always differ slightly from those of Harris (1963), p. 5.)

Type
Research Article
Copyright
Copyright © Applied Probability Trust 

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