Almost sure central limit theorem for branching random walks in random environment

Makoto Nakashima

doi:10.1214/10-aap699

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arXiv · 1101.1176

Almost sure central limit theorem for branching random walks in random environment

Makoto Nakashima

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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 $d\geq3$ 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. 2011-01-06. Almost sure central limit theorem for branching random walks in random environment. https://doi.org/10.1214/10-aap699

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