Electronic Communications in Probability

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

Nadine Guillotin-Plantard, Yueyun Hu, and Bruno Schapira

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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

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

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

Random walk in random scenery Weak limit theorem Law of the iterated logarithm Brownian motion in Brownian Scenery Strong approximation

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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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