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Chernoff's theorem in the branching random walk

Published online by Cambridge University Press:  14 July 2016

J. D. Biggins
J. D. Biggins*
Affiliation:
University of Sheffield
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Abstract

If Fn∗ is the n-fold Stieltjes convolution of the increasing function F, then a version of Chernoff's theorem, on the limiting behaviour of (Fn∗(na))1/n, is established for Fn∗. If Z(n)(t) is the number of the nth-generation people to the left of t in a supercritical branching random walk then an analogous result is proved for Z(n).

Keywords

CHERNOFF'S THEOREMBRANCHING RANDOM WALKBRANCHING PROCESSES
Type
Short Communications
Information
Journal of Applied Probability , Volume 14 , Issue 3 , September 1977 , pp. 630 - 636
Copyright
Copyright © Applied Probability Trust 1977 

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