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Martingale convergence in the branching random walk

Published online by Cambridge University Press:  14 July 2016

J. D. Biggins
J. D. Biggins*
Affiliation:
University of Oxford
*
*Now at the University of Sheffield.
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Abstract

A result like the Kesten-Stigum theorem is obtained for certain martingales associated with the branching random walk. A special case, when a ‘Malthusian parameter’ exists, is considered in greater detail and a link with some known results about the Crump-Mode model for a population is established.

Keywords

BRANCHING RANDOM WALKSMARTINGALESFUNCTIONAL EQUATIONBRANCHING PROCESSES
Type
Research Papers
Information
Journal of Applied Probability , Volume 14 , Issue 1 , March 1977 , pp. 25 - 37
Copyright
Copyright © Applied Probability Trust 1977 

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