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.
Publié le : 2011-02-15
Classification:
Branching random walk,
random environment,
central limit theorem,
linear stochastic evolutions,
phase transition,
60K37,
60K35,
60F05,
60J80,
60K35,
82D30
@article{1292598038,
author = {Nakashima, Makoto},
title = {Almost sure central limit theorem for branching random walks in random environment},
journal = {Ann. Appl. Probab.},
volume = {21},
number = {1},
year = {2011},
pages = { 351-373},
language = {en},
url = {http://dml.mathdoc.fr/item/1292598038}
}
Nakashima, Makoto. Almost sure central limit theorem for branching random walks in random environment. Ann. Appl. Probab., Tome 21 (2011) no. 1, pp. 351-373. http://gdmltest.u-ga.fr/item/1292598038/