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November 2007 A functional CLT for the occupation time of a state-dependent branching random walk
Matthias Birkner, Iljana Zähle
Ann. Probab. 35(6): 2063-2090 (November 2007). DOI: 10.1214/009117907000000150

Abstract

We show that the centred occupation time process of the origin of a system of critical binary branching random walks in dimension d≥3, started off either from a Poisson field or in equilibrium, when suitably normalized, converges to a Brownian motion in d≥4. In d=3, the limit process is a fractional Brownian motion with Hurst parameter 3/4 when starting in equilibrium, and a related Gaussian process when starting from a Poisson field. For (dependent) branching random walks with state dependent branching rate we obtain convergence in f.d.d. to the same limit process, and for d=3 also a functional limit theorem.

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Matthias Birkner. Iljana Zähle. "A functional CLT for the occupation time of a state-dependent branching random walk." Ann. Probab. 35 (6) 2063 - 2090, November 2007. https://doi.org/10.1214/009117907000000150

Information

Published: November 2007
First available in Project Euclid: 8 October 2007

zbMATH: 1128.60083
MathSciNet: MR2353383
Digital Object Identifier: 10.1214/009117907000000150

Subjects:
Primary: 60K35

Rights: Copyright © 2007 Institute of Mathematical Statistics

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Vol.35 • No. 6 • November 2007
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