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The sequential empirical process of a random walk in random scenery

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  • Wendler, Martin

Abstract

A random walk in random scenery (Yn)n∈N is given by Yn=ξSn for a random walk (Sn)n∈N and i.i.d. random variables (ξn)n∈Z. In this paper, we will show the weak convergence of the sequential empirical process, i.e. the centered and rescaled empirical distribution function. The limit process shows a new type of behavior, combining properties of the limit in the independent case (roughness of the paths) and in the long range dependent case (self-similarity).

Suggested Citation

  • Wendler, Martin, 2016. "The sequential empirical process of a random walk in random scenery," Stochastic Processes and their Applications, Elsevier, vol. 126(9), pages 2787-2799.
    • Handle: RePEc:eee:spapps:v:126:y:2016:i:9:p:2787-2799
    DOI: 10.1016/j.spa.2016.03.002
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    References listed on IDEAS

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    1. Khoshnevisan, Davar & Lewis, Thomas M., 1998. "A law of the iterated logarithm for stable processes in random scenery," Stochastic Processes and their Applications, Elsevier, vol. 74(1), pages 89-121, May.
    2. Berkes, István & Hörmann, Siegfried & Schauer, Johannes, 2009. "Asymptotic results for the empirical process of stationary sequences," Stochastic Processes and their Applications, Elsevier, vol. 119(4), pages 1298-1324, April.
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