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The almost sure central limit theorem for one-dimensional nearest-neighbour random walks in a space-time random environment

Published online by Cambridge University Press:  14 July 2016

Jean Bérard*
Affiliation:
Université Claude Bernard Lyon 1
*
Postal address: Laboratoire de Probabilités, Combinatoire et Statistique, Université Claude Bernard Lyon 1, 50, avenue Tony Garnier, 69366 Lyon Cedex 07, France. Email address: jean.berard@univ-lyon1.fr

Abstract

The central limit theorem for random walks on ℤ in an i.i.d. space-time random environment was proved by Bernabei et al. for almost all realization of the environment, under a small randomness assumption. In this paper, we prove that, in the nearest-neighbour case, when the averaged random walk is symmetric, the almost sure central limit theorem holds for an arbitrary level of randomness.

Type
Research Papers
Copyright
Copyright © Applied Probability Trust 2004 

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