Electronic Communications in Probability

Reconstructing the environment seen by a RWRE

Nina Gantert and Jan Nagel

Full-text: Open access

Abstract

Consider a walker performing a random walk in an i.i.d. random environment, and assume that the walker tells us at each time the environment it sees at its present location. Given this history of the transition probabilities seen from the walker - but not its trajectory - can we reconstruct the law of the environment? We show that in a one-dimensional environment, the law of the environment can be reconstructed. This model can be seen as a special case of a scenery reconstruction problem, where the steps of the random walker depend on the scenery.<br />

Article information

Source
Electron. Commun. Probab., Volume 19 (2014), paper no. 27, 9 pp.

Dates
Accepted: 7 May 2014
First available in Project Euclid: 7 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1465316729

Digital Object Identifier
doi:10.1214/ECP.v19-3013

Mathematical Reviews number (MathSciNet)
MR3208325

Zentralblatt MATH identifier
1312.60119

Subjects
Primary: 60K37: Processes in random environments
Secondary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)

Keywords
random walk in random environment scenery reconstruction

Rights
This work is licensed under a Creative Commons Attribution 3.0 License.

Citation

Gantert, Nina; Nagel, Jan. Reconstructing the environment seen by a RWRE. Electron. Commun. Probab. 19 (2014), paper no. 27, 9 pp. doi:10.1214/ECP.v19-3013. https://projecteuclid.org/euclid.ecp/1465316729


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