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

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  • Chenavier, Nicolas
  • Darwiche, Ahmad

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.

Suggested Citation

  • Chenavier, Nicolas & Darwiche, Ahmad, 2020. "Extremes for transient random walks in random sceneries under weak independence conditions," Statistics & Probability Letters, Elsevier, vol. 158(C).
    • Handle: RePEc:eee:stapro:v:158:y:2020:i:c:s0167715219303037
    DOI: 10.1016/j.spl.2019.108657
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    1. Franke, Brice & Saigo, Tatsuhiko, 2009. "The extremes of a random scenery as seen by a random walk in a random environment," Statistics & Probability Letters, Elsevier, vol. 79(8), pages 1025-1030, April.
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