Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1155400 | Stochastic Processes and their Applications | 2016 | 13 Pages |
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).
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Martin Wendler,