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On asymptotic properties of sub-critical branching processes

Published online by Cambridge University Press:  09 April 2009

E. Seneta
Affiliation:
Australian National UniversityCanberra
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Let Zn be the numer of individuals in the nth generation of a discrete branching process, descended from a single a singel ancestor, for which we put It is well known that the probability generating function of Zn is Fn(s), the n-th functional iterate of F(s), and that if m = EZ1 does not exceed unity, then lim (Harris [1], Chapter 1). In particular, extinction is certain.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1968

References

[1]Harris, T. E., The Theory of Branching Processes (Springer-Verlag, Berlin, 1963).CrossRefGoogle Scholar
[2]Heathcote, C. R. and Seneta, E., ‘Inequalities for branching processes’, J. Appl. Prob. 3 (1966), 261–7. (See also correction: 4 (1967), 215.)CrossRefGoogle Scholar
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[4]Seneta, E., ‘On the transient behaviour of a Poisson branching process’, J. Aust. Math. Soc. 7 (1967), 465–80.CrossRefGoogle Scholar
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