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A connection between the limit and the maximum random variable of a branching process in varying environments

Published online by Cambridge University Press:  14 July 2016

F. C. Klebaner  and
H.-J. Schuh
F. C. Klebaner*
Affiliation:
University of Melbourne
H.-J. Schuh*
Affiliation:
University of Melbourne
*
∗Postal address: Department of Statistics, Richard Berry Building, University of Melbourne, Parkville, VIC 3052, Australia.
∗Postal address: Department of Statistics, Richard Berry Building, University of Melbourne, Parkville, VIC 3052, Australia.
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Abstract

We show for a certain class of Galton–Watson branching processes in varying environments (Zn)n that moments of the maximum random variable supnZn/Cn exist if and only if the same moments of limnZn/Cn exist, where Cn is a sequence of suitable constants.

Keywords

SUPERCRITICAL GALTON-WATSON BRANCHING PROCESS IN VARYING ENVIRONMENTSEXTINCTION PROBABILITYNORMALIZING CONSTANTSLIMIT RANDOM VARIABLEMAXIMUM RANDOM VARIABLEMOMENTS
Type
Short Communications
Information
Journal of Applied Probability , Volume 19 , Issue 3 , September 1982 , pp. 681 - 684
Copyright
Copyright © Applied Probability Trust 1982 

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References

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