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A theorem on compositions of random probability generating functions and applications to branching processes with random environments

Published online by Cambridge University Press:  14 July 2016

Norman Kaplan
Norman Kaplan*
Affiliation:
University of California, Berkeley
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Abstract

The results of this paper deal directly with the behavior of compositions of random probability generating functions. These results are then applied to the theory of branching processes with random environments. In particular, it is shown that it is not possible to strengthen many of the existing limit theorems on this subject.

Keywords

BRANCHING PROCESSBRANCHING PROCESS WITH RANDOM ENVIRONMENTRANDOM ENVIRONMENTRANDOM PROBABILITY GENERATING FUNCTIONS
Type
Research Papers
Information
Journal of Applied Probability , Volume 9 , Issue 1 , March 1972 , pp. 1 - 12
Copyright
Copyright © Applied Probability Trust 1972 

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References

[1] Athreya, K. B. and Karlin, S. (1971) Branching processes with random environments, I: Extinction probability. To appear.Google Scholar
[2] Athreya, K. B. and Karlin, S. (1971) Branching processes with random environments. II: Limit theorems. To appear.CrossRefGoogle Scholar
[3] Breiman, L. (1958) An elementary theorem concerning stationary ergodic processes Ann. Math. Statist. 29, 592–595.Google Scholar
[4] Feller, W. (1966) An Introduction to Probability Theory and its Applications, Vol. 2, John Wiley, New York.Google Scholar
[5] Harris, T. E. (1963) The Theory of Branching Processes. Springer-Verlag, Berlin.Google Scholar
[6] Kaplan, N. (1970) Topics in the Theory of Branching Processes with Random Environments. , Stanford University.Google Scholar
[7] Kaplan, N. (1971) A note on a supercritical B.P.R.E. To appear.Google Scholar
[8] Smith, W. L. and Wilkinson, W. (1969) On branching processes in random environments. Ann. Math. Statist. 40, 814–827.Google Scholar