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On constant tail behaviour for the limiting random variable in a supercritical branching process

Part of: Markov processes

Published online by Cambridge University Press:  14 July 2016

B. M. Hambly
B. M. Hambly*
Affiliation:
University of Edinburgh
*
∗ Postal address: Department of Mathematics and Statistics, University of Edinburgh, King's Buildings, Mayfield Road, Edinburgh EH9 3JZ, UK.
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Abstract

We examine a family of supercritical branching processes and compute the density of the limiting random variable, W, for their normalized population size. In this example the left tail of W decays exponentially and there is no oscillation in this tail as typically observed. The branching process is embedded in the n-adic rational random walk approximation to Brownian motion on [0, 1]. This connection allows the explicit computation of the density of W.

Keywords

BROWNIAN MOTIONSIERPINSKI GASKET

MSC classification

Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Secondary: 60J65: Brownian motion

Information

Type
Short Communications
Information
Journal of Applied Probability , Volume 32 , Issue 1 , March 1995 , pp. 267 - 273
Copyright
Copyright © Applied Probability Trust 1995 

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References

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