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On constant tail behaviour for the limiting random variable in a supercritical branching process
Published online by Cambridge University Press: 14 July 2016
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.
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- Copyright © Applied Probability Trust 1995
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