The sequential empirical process of a random walk in random scenery - Wendler, Martin (Technische Universität Dortmund, 2014)
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).
Discussion Paper / SFB 823;32/2014
Keywords: random walk; empirical process; random scenery; 310; 330; 620