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

Journal of Applied Probability / Volume 9 / Issue 1 / March 1972

Published online by Cambridge University Press:

14 July 2016, pp. 1-12

Print publication:

March 1972
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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.

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