An almost sure invariance principle for random walks in a space-time random environment

We consider a discrete time random walk in a space-time i.i.d. random environment. We use a martingale approach to show that the walk is diffusive in almost every fixed environment. We improve on existing results by proving an invariance principle and considering environments with an L2 averaged dri...

Full description

Saved in:
Bibliographic Details
Published in:Probability theory and related fields 2005-11, Vol.133 (3), p.299-314
Main Authors: RASSOUL-AGHA, Firas, SEPPÄLÄINEN, Timo
Format: Article
Language:English
Subjects:
Brownian motion
Central limit theorem
Digital Object Identifier
Exact sciences and technology
Hypotheses
Invariance
Limit theorems
Martingales
Mathematics
Noise
Probability
Probability and statistics
Probability theory and stochastic processes
Random walk
Random walk theory
Sciences and techniques of general use
Spacetime
Special processes (renewal theory, markov renewal processes, semi-markov processes, statistical mechanics type models, applications)
Stochastic processes
Studies
Theorems
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We consider a discrete time random walk in a space-time i.i.d. random environment. We use a martingale approach to show that the walk is diffusive in almost every fixed environment. We improve on existing results by proving an invariance principle and considering environments with an L2 averaged drift. We also state an a.s. invariance principle for random walks in general random environments whose hypothesis requires a subdiffusive bound on the variance of the quenched mean, under an ergodic invariant measure for the environment chain. [PUBLICATION ABSTRACT]
ISSN:0178-8051
1432-2064
DOI:10.1007/s00440-004-0424-1