Extremes for transient random walks in random sceneries under weak independence conditions

Abstract

Let {ξ(k), k ∈ Z} be a stationary sequence of random variables with conditions of type D(u n ) and D ′ (u n ). Let {S n , n ∈ N} be a transient random walk in the domain of attraction of a stable law. We provide a limit theorem for the maximum of the first n terms of the sequence {ξ(S n ), n ∈ N} as n goes to infinity. This paper extends a result due to Franke and Saigo who dealt with the case where the sequence {ξ(k), k ∈ Z} is i.i.d.