Hostname: page-component-74656f9884-2dmjx Total loading time: 0 Render date: 2026-11-10T05:14:12.039Z Has data issue: false hasContentIssue false
  • English
  • Français

A note on the branching random walk

Published online by Cambridge University Press:  14 July 2016

Norman Kaplan
Norman Kaplan*
Affiliation:
National Institute of Environmental Health Sciences
*
∗ Postal address: Biometry Branch, National Institute of Environmental Health Sciences, P.O. Box 12233, Research Triangle Park, NC 27709, U.S.A.
Get access Rights & Permissions [Opens in a new window]

Abstract

A well-known theorem in the theory of branching random walks is shown to hold when only Σj log jpj <∞. This result was asserted by Athreya and Kaplan (1978), but their proof was incorrect.

Keywords

BRANCHING RANDOM WALK

Information

Type
Short Communications
Information
Journal of Applied Probability , Volume 19 , Issue 2 , June 1982 , pp. 421 - 424
Copyright
Copyright © Applied Probability Trust 1982 

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.)

Article purchase

Temporarily unavailable

References

Athreya, K. B. and Kaplan, N. (1978) Additive property and its application in branching processes. In Branching Processes, Dekker, New York, 27–60.Google Scholar
Athreya, K. B. and Ney, P. (1972) Branching Processes. Springer-Verlag, Berlin.Google Scholar
Baum, L. E. and Katz, M. (1963) Convergence rates in the law of large numbers. Bull. Amer. Math. Soc. 69, 771–773.Google Scholar
Feller, W. (1966) An Introduction to Probability Theory and its Applications, Vol. II. Wiley, New York.Google Scholar
Kaplan, N. and Asmussen, S. (1976) Branching random walks II. Stoch. Proc. Appl. 4, 15–31.Google Scholar
Kesten, H. and Stigum, B. P. (1967) Limit theorems for decomposable multi-dimensional Galton–Watson processes. J. Math. Anal. Appl. 17, 309–338.CrossRefGoogle Scholar