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

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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