%0 Journal Article
%T Convergence of dependent walks in a random scenery to fBm-local time fractional stable motions
%A Serge Cohen
%A Cl¨Śment Dombry
%J Mathematics
%D 2008
%I arXiv
%X It is classical to approximate the distribution of fractional Brownian motion by a renormalized sum $ S_n $ of dependent Gaussian random variables. In this paper we consider such a walk $ Z_n $ that collects random rewards $ \xi_j $ for $ j \in \mathbb Z,$ when the ceiling of the walk $ S_n $ is located at $ j.$ The random reward (or scenery) $ \xi_j $ is independent of the walk and with heavy tail. We show the convergence of the sum of independent copies of $ Z_n$ suitably renormalized to a stable motion with integral representation, whose kernel is the local time of a fractional Brownian motion (fBm). This work extends a previous work where the random walk $ S_n$ had independent increments limits.
%U http://arxiv.org/abs/0805.3054v1