## Electronic Communications in Probability

### The quenched limiting distributions of a one-dimensional random walk in random scenery

#### Abstract

For a one-dimensional random walk in random scenery (RWRS) on Z, we determine its quenched weak limits by applying Strassen's functional law of iterated logarithm. As a consequence, conditioned on the random scenery, the one dimensional RWRS does not converge in law, in contrast with the multi-dimensional case.

#### Article information

Source
Electron. Commun. Probab., Volume 18 (2013), paper no. 85, 7 pp.

Dates
Accepted: 3 November 2013
First available in Project Euclid: 7 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1465315624

Digital Object Identifier
doi:10.1214/ECP.v18-2918

Mathematical Reviews number (MathSciNet)
MR3141794

Zentralblatt MATH identifier
1329.60027

Subjects
Primary: 60F05: Central limit and other weak theorems
Secondary: 60G52: Stable processes

Rights

#### Citation

Guillotin-Plantard, Nadine; Hu, Yueyun; Schapira, Bruno. The quenched limiting distributions of a one-dimensional random walk in random scenery. Electron. Commun. Probab. 18 (2013), paper no. 85, 7 pp. doi:10.1214/ECP.v18-2918. https://projecteuclid.org/euclid.ecp/1465315624

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