Random walks in random environment: What a single trajectory tells

We present a procedure that determines the law of a random walk in an iid random environment as a function of a single “typical” trajectory. We indicate when the trajectory characterizes the law of the environment, and we say how this law can be determined. We then show how independent trajectories...

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Bibliographic Details
Published in:Israel journal of mathematics 2004-01, Vol.142 (1), p.205-220
Main Authors: Adelman, Omer, Enriquez, Nathanaël
Format: Article
Language:English
Subjects:
Environmental law
Mathematics
Probability
Random walk
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Summary:We present a procedure that determines the law of a random walk in an iid random environment as a function of a single “typical” trajectory. We indicate when the trajectory characterizes the law of the environment, and we say how this law can be determined. We then show how independent trajectories having the distribution of the original walk can be generated as functions of the single observed trajectory.
ISSN:0021-2172
1565-8511
DOI:10.1007/BF02771533