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February 2011 Almost sure central limit theorem for branching random walks in random environment
Makoto Nakashima
Ann. Appl. Probab. 21(1): 351-373 (February 2011). DOI: 10.1214/10-AAP699

Abstract

We consider the branching random walks in d-dimensional integer lattice with time–space i.i.d. offspring distributions. Then the normalization of the total population is a nonnegative martingale and it almost surely converges to a certain random variable. When d≥3 and the fluctuation of environment satisfies a certain uniform square integrability then it is nondegenerate and we prove a central limit theorem for the density of the population in terms of almost sure convergence.

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Makoto Nakashima. "Almost sure central limit theorem for branching random walks in random environment." Ann. Appl. Probab. 21 (1) 351 - 373, February 2011. https://doi.org/10.1214/10-AAP699

Information

Published: February 2011
First available in Project Euclid: 17 December 2010

zbMATH: 1210.60108
MathSciNet: MR2759206
Digital Object Identifier: 10.1214/10-AAP699

Subjects:
Primary: 60K37
Secondary: 60F05, 60J80, 60K35, 60K35, 82D30

Rights: Copyright © 2011 Institute of Mathematical Statistics

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Vol.21 • No. 1 • February 2011
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