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Functional equations and the Galton-Watson process

Published online by Cambridge University Press:  01 July 2016

E. Seneta
E. Seneta*
Affiliation:
Australian National University
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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 < f 0 ≡ F(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.)

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Research Article
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Advances in Applied Probability , Volume 1 , Issue 1 , Spring 1969, pp. 1 - 42
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Copyright © Applied Probability Trust 

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