Functional equations and the Galton-Watson process
1969; Cambridge University Press; Volume: 1; Issue: 01 Linguagem: Inglês
10.1017/s0001867800036880
ISSN1475-6064
Autores Tópico(s)Evolution and Genetic Dynamics
ResumoIn 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 f j ≠ 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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