Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-28T17:06:01.208Z Has data issue: false hasContentIssue false
  • English
  • Français

An upper bound for the mean of Yaglom's limit

Published online by Cambridge University Press:  14 July 2016

Lawrence S. Evans
Lawrence S. Evans*
Affiliation:
Roosevelt University, Chicago, Illinois
Get access Rights & Permissions [Opens in a new window]

Abstract

For a single-type Galton—Watson branching process with mean less than one and finite second moment, we establish an upper bound for the mean of the associated Yaglom limit. This bound is attained if and only if the generating function of the process is linear.

Keywords

BRANCHING PROCESSYAGLOM LIMIT
Type
Short Communications
Information
Journal of Applied Probability , Volume 15 , Issue 1 , March 1978 , pp. 199 - 201
Copyright
Copyright © Applied Probability Trust 1978 

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.)

References

[1] Athreya, K. B. and Ney, P. (1972) Branching Processes. Springer, Berlin.CrossRefGoogle Scholar
[2] Bingham, N. H. and Doney, R. A. (1974) Asymptotic properties of supercritical branching processes I: the Galton—Watson process. Adv. Appl. Prob. 6, 711–731.CrossRefGoogle Scholar
[3] Harris, T. E. (1963) The Theory of Branching Processes. Springer, Berlin.Google Scholar
[4] Jagers, P. (1975) Branching Processes with Biological Applications. Wiley, New York.Google Scholar
[5] Joffe, A. (1967) On the Galton—Watson branching process with mean less than one. Ann. Math. Statist. 38, 264–266.CrossRefGoogle Scholar
[6] Yaglom, A. M. (1947) Certain limit theorems of the theory of branching random processes (In Russian). Soviet Math. Doklady 56, 795–798.Google Scholar