Functional equations and the Galton-Watson process
- 1 January 1969
- journal article
- research article
- Published by Cambridge University Press (CUP) in Advances in Applied Probability
- Vol. 1 (01) , 1-42
- https://doi.org/10.1017/s0001867800036880
Abstract
In the present exposition we are concerned only with the simple Galton-Watson process, initiated by a single ancestor (Harris (1963), Chapter I). Letdenote the probability generating function of the offspring distribution of a single individual. Our fundamental assumption, which holds throughout the sequel, is thatfj≠ 1,j= 0,1,2, …; in particular circumstances it shall be necessary to strengthen this to 0 <f0≡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.)Keywords
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