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Journal Articles Statistics and Probability Letters Year : 2020

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.
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Dates and versions

hal-03488617 , version 1 (20-07-2022)

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Attribution - NonCommercial

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Nicolas Chenavier, Ahmad Darwiche. Extremes for transient random walks in random sceneries under weak independence conditions. Statistics and Probability Letters, 2020, 158, pp.108657. ⟨10.1016/j.spl.2019.108657⟩. ⟨hal-03488617⟩
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