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A branching process with a state dependent immigration component

Published online by Cambridge University Press:  01 July 2016

A. G. Pakes
A. G. Pakes*
Affiliation:
Monash University
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Extract

Consider the well known Galton-Watson branching process (Harris (1963)) in which individuals reproduce independently of each other and have probability a j (j = 0, 1, · · ·) of giving rise to j individuals in the next generation. In recent years some attention has been given to the branching process in which there is an independent immigration component at each generation, b j (j = 0, 1, · · ·) being the probability of j immigrants entering each generation. For a review of this work see Seneta (1969), and Pakes (1971 a, b and c) for further results.

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Type
Research Article
Information
Advances in Applied Probability , Volume 3 , Issue 2 , Autumn 1971 , pp. 301 - 314
Copyright
Copyright © Applied Probability Trust 1971 

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