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(un) and D′(un). Let {Sn,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(Sn),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.