Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-23T17:50:03.287Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
Get access Rights & Permissions [Opens in a new window]

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 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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