Open Access
2009 A functional approach for random walks in random sceneries
Clement Dombry, Nadine Guillotin-Plantard
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Electron. J. Probab. 14: 1495-1512 (2009). DOI: 10.1214/EJP.v14-659


A functional approach for the study of the random walks in random sceneries (RWRS) is proposed. Under fairly general assumptions on the random walk and on the random scenery, functional limit theorems are proved. The method allows to study separately the convergence of the walk and of the scenery: on the one hand, a general criterion for the convergence of the local time of the walk is provided, on the other hand, the convergence of the random measures associated with the scenery is studied. This functional approach is robust enough to recover many of the known results on RWRS as well as new ones, including the case of many walkers evolving in the same scenery.


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Clement Dombry. Nadine Guillotin-Plantard. "A functional approach for random walks in random sceneries." Electron. J. Probab. 14 1495 - 1512, 2009.


Accepted: 2 July 2009; Published: 2009
First available in Project Euclid: 1 June 2016

zbMATH: 1195.60129
MathSciNet: MR2519528
Digital Object Identifier: 10.1214/EJP.v14-659

Primary: 60F05
Secondary: 60F25 , 60G50

Keywords: Local time , Random scenery , Random walk , weak convergence

Vol.14 • 2009
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