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Annals of Probability 41, 2 (2013) 619-635
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Recurrence rates and hitting-time distributions for random walks on the line
Francoise Pene 1, Benoît Saussol ( ) 1, Roland Zweimüller 2

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.
1:  Laboratoire de mathématiques de Brest (LM)
CNRS : UMR6205 – Université de Bretagne Occidentale (UBO) – Institut Supérieur des Sciences et Technologies de Brest (ISSTB)
2:  Fakultät für Mathematik
Universität Wien
random walk – recurrence rate – hitting-time distribution
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