Almost sure central limit theorem for branching random walks in random environment
Probability
2011-01-07 v1
Abstract
We consider the branching random walks in -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 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.
Cite
@article{arxiv.1101.1176,
title = {Almost sure central limit theorem for branching random walks in random environment},
author = {Makoto Nakashima},
journal= {arXiv preprint arXiv:1101.1176},
year = {2011}
}
Comments
Published in at http://dx.doi.org/10.1214/10-AAP699 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)