A functional approach for random walks in random sceneries

Clément Dombry (1) , Nadine Guillotin-Plantard (2, 3)

1 LMA [Poitiers] - Laboratoire de mathématiques et applications [UMR 6086]
2 UCBL - Université Claude Bernard Lyon 1
3 ICJ - Institut Camille Jordan

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.

Mots clés: random walk; random scenery; local time; limit theorem

Domaines: Probabilités [math.PR]

Clément Dombry, Nadine Guillotin-Plantard. A functional approach for random walks in random sceneries. Electronic Journal of Probability, 2009, pp.Vol. 14, No 50, 1495--1512. ⟨hal-00366134⟩