Exponential rate of almost-sure convergence of intrinsic martingales in supercritical branching random walks
Alexander Iksanov and Matthias Meiners
Source: J. Appl. Probab. Volume 47, Number 2
(2010), 513-525.
Abstract
We provide sufficient conditions which ensure that the intrinsic martingale in the supercritical branching random walk converges exponentially fast to its limit. We include in particular the case of Galton-Watson processes so that our results can be seen as a generalization of a result given in the classical treatise by Asmussen and Hering (1983). As an auxiliary tool, we prove ultimate versions of two results concerning the exponential renewal measures which may be of interest in themselves and which correct, generalize, and simplify some earlier works.
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.jap/1276784906
Digital Object Identifier: doi:10.1239/jap/1276784906
Zentralblatt MATH identifier: 05758484
Mathematical Reviews number (MathSciNet): MR2668503
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