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A theorem on discrete time branching processes allowing immigration

Published online by Cambridge University Press:  14 July 2016

John F. Reynolds
John F. Reynolds*
Affiliation:
University College, Cardiff
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Extract

We consider a population which evolves at discrete points in time by branching and immigration, and in which each member reproduces independently of all others. Let Fn(x) denote the probability generating function (P.G.F.) of the number of offspring produced by each member of the nth generation, Bn–1(x) the P.G.F. of the number of immigrants joining the nth generation and Zn the population size in the nth generation. We write

Type
Short Communications
Information
Journal of Applied Probability , Volume 7 , Issue 2 , August 1970 , pp. 446 - 450
Copyright
Copyright © Applied Probability Trust 1970 

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