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

Part of: Markov processes Limit theorems Special processes Combinatorics

Published online by Cambridge University Press:  14 July 2016

Jean Bérard
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
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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.

Keywords

Random walkrandom environmentcentral limit theoremgenerating function

MSC classification

Primary: 60F05: Central limit and other weak theorems 60J10: Markov chains (discrete-time Markov processes on discrete state spaces) 60K37: Processes in random environments 05A15: Exact enumeration problems, generating functions
Type
Research Papers
Information
Journal of Applied Probability , Volume 41 , Issue 1 , March 2004 , pp. 83 - 92
Copyright
Copyright © Applied Probability Trust 2004 

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References

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