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arXiv · 1003.5073

Recurrence rates and hitting-time distributions for random walks on the line

Francoise Pene·Benoît Saussol·Roland Zweimüller
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Abstract

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.

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Francoise Pene, Benoît Saussol, Roland Zweimüller. 2010-03-26. Recurrence rates and hitting-time distributions for random walks on the line. https://doi.org/10.1214/11-aop698

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