## Electronic Communications in Probability

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

### Reconstructing the environment seen by a RWRE

#### 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