Article ID Journal Published Year Pages File Type
1155400 Stochastic Processes and their Applications 2016 13 Pages PDF
Abstract

A random walk in random scenery (Yn)n∈N(Yn)n∈N is given by Yn=ξSnYn=ξSn for a random walk (Sn)n∈N(Sn)n∈N and i.i.d. random variables (ξn)n∈Z(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).

Related Topics
Physical Sciences and Engineering Mathematics Mathematics (General)
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