%0 Journal Article
%T Recurrence rates and hitting-time distributions for random walks on the line
%A Francoise Pene
%A Beno£¿t Saussol
%A Roland Zweim¨¹ller
%J Mathematics
%D 2010
%I arXiv
%R 10.1214/11-AOP698
%X We consider random walks on the line given by a sequence of independent identically distributed jumps belonging to the strict domain of attraction of a stable distribution, and first determine the almost sure exponential divergence rate, as r goes to zero, of the return time to (-r,r). We then refine this result by establishing a limit theorem for the hitting-time distributions of (x-r,x+r) with arbitrary real x.
%U http://arxiv.org/abs/1003.5073v2