Abstract.
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.
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T. Seppäläinen was partially supported by National Science Foundation grant DMS-0402231.
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Rassoul-Agha, F., Seppäläinen, T. An almost sure invariance principle for random walks in a space-time random environment. Probab. Theory Relat. Fields 133, 299–314 (2005). https://doi.org/10.1007/s00440-004-0424-1
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DOI: https://doi.org/10.1007/s00440-004-0424-1
Keywords
- Stochastic Process
- Random Walk
- Probability Theory
- Discrete Time
- Invariant Measure
Ser. A 49, 275–287 (1987)