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On the almost sure convergence of controlled branching processes

Published online by Cambridge University Press:  14 July 2016

J. H. Bagley*
Affiliation:
University of Manchester Institute of Science and Technology
*
Postal address: Department of Mathematics, UMIST, P.O. Box 88, Manchester M60 1QD, UK.

Abstract

An almost sure convergence result for the normed population size of a supercritical controlled branching process is proved.

Type
Short Communications
Copyright
Copyright © Applied Probability Trust 1986 

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References

[1] Asmussen, S. (1978) Some martingale methods in the limit theory of supercritical branching processes. In Branching Processes, eds. Joffe, A. and Ney, P., Marcel Dekker, New York.Google Scholar
[2] Chow, Y. S. and Teicher, H. (1978) Probability Theory: Independence, Interchangeability, Martingales. Springer-Verlag, New York.Google Scholar
[3] Foster, J. I. (1971) A limit theorem for a branching process with state-independent immigration. Ann. Math. Statist. 42, 17731776.Google Scholar
[4] Jagers, P. (1975) Branching Processes with Biological Applications. Wiley, New York.Google Scholar
[5] Sevastyanov, B. A. and Zubkov, A. M. (1974) Controlled branching processes. Theory Prob. Appl. 19, 1424.CrossRefGoogle Scholar
[6] Stout, W. F. (1974) Almost Sure Convergence. Academic Press, London.Google Scholar
[7] Zubkov, A. M. (1974) Analogies between Galton–Watson processes and ? -branching processes. Theory Prob. Appl. 19, 309331.CrossRefGoogle Scholar