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On a result of Rubin and Vere-Jones concerning subcritical branching processes

Published online by Cambridge University Press:  14 July 2016

Fred M. Hoppe*
Affiliation:
University of Alberta, Edmonton

Abstract

If a subcritical Galton-Watson process is initiated with an arbitrary mass distribution, then it is known that under certain conditions proper conditional limit distributions exist, depending on a single parameter. It is shown here that there is a one-to-one correspondence between these distributions and those arising from the process with a linear offspring probability generating function.

Type
Short Communications
Copyright
Copyright © Applied Probability Trust 1976 

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References

[1] Heathcote, C. R., Seneta, E. and Vere-Jones, D. (1967) A refinement of two theorems in the theory of branching processes. Theor. Prob. Appl. 12, 341346.Google Scholar
[2] Hoppe, F. (1975a) Functional Equations with Applications to Multitype Galton-Watson Branching Processes. Ph.D. dissertation, Princeton University.Google Scholar
[3] Hoppe, F. (1975b) Stationary measures for multitype branching processes. J. Appl. Prob. 12, 219227.CrossRefGoogle Scholar
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