The sequential empirical process of a random walk in random scenery
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Date
2014-10-09
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Abstract
A random walk in random scenery (Yn)n2N is given by Yn = Sn
for a random walk (Sn)n2N and iid random variables ( (n))n2N. 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 form independent
case (roughness of the paths) and of the long range dependent case (self-
similarity).
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Keywords
random walk, empirical process, random scenery