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December 2016 A central limit theorem and a law of the iterated logarithm for the Biggins martingale of the supercritical branching random walk
Alexander Iksanov, Zakhar Kabluchko
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J. Appl. Probab. 53(4): 1178-1192 (December 2016).

Abstract

Let (Wn(θ))n∈ℕ0 be the Biggins martingale associated with a supercritical branching random walk, and denote by W_(θ) its limit. Assuming essentially that the martingale (Wn(2θ))n∈ℕ0 is uniformly integrable and that var W1(θ) is finite, we prove a functional central limit theorem for the tail process (W(θ)-Wn+r(θ))r∈ℕ0 and a law of the iterated logarithm for W(θ)-Wn(θ) as n→∞.

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Alexander Iksanov. Zakhar Kabluchko. "A central limit theorem and a law of the iterated logarithm for the Biggins martingale of the supercritical branching random walk." J. Appl. Probab. 53 (4) 1178 - 1192, December 2016.

Information

Published: December 2016
First available in Project Euclid: 7 December 2016

zbMATH: 1356.60055
MathSciNet: MR3581250

Subjects:
Primary: 60G42
Secondary: 60J80

Rights: Copyright © 2016 Applied Probability Trust

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Vol.53 • No. 4 • December 2016
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