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Moments of the maximum in a critical branching process

Published online by Cambridge University Press:  14 July 2016

Howard Weiner
Howard Weiner*
Affiliation:
University of California at Davis
*
∗Postal address: Department of Mathematics, University of California, Davis, CA 95616, USA.
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Abstract

Let Zn denote the number of cells at time n in a critical discrete-time Galton–Watson branching process with finite offspring variance. Let Martingale arguments are used to show that for some 0<a≦b<∞

Keywords

MEAN LOGARITHMIC GROWTHMARTINGALE INEQUALITIES
Type
Short Communications
Information
Journal of Applied Probability , Volume 21 , Issue 4 , December 1984 , pp. 920 - 923
Copyright
Copyright © Applied Probability Trust 1984 

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Footnotes

Research partially supported at Stanford University under ONR Contract N00014-76-C-0475.

References

[1] Athreya, K. and Ney, P. E. (1972) Branching Processes. Springer-Verlag, New York.CrossRefGoogle Scholar
[2] Chow, Y. S. and Teicher, H. (1978) Probability Theory. Springer-Verlag, New York.CrossRefGoogle Scholar
[3] Klebaner, F. C. and Schuh, H.-J. (1982) A connection between the limit and the maximum random variable of a branching process in varying environments. J. Appl. Prob. 19, 681–684.CrossRefGoogle Scholar