The sequential empirical process of a random walk in random scenery

Martin Wendler

Stochastic Processes and their Applications, 2016, vol. 126, issue 9, 2787-2799

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).

Keywords: Random walk; Random scenery; Empirical process (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1016/j.spa.2016.03.002

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