## The Annals of Probability

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

#### 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 $\varepsilon\to0$, of the return time to $(-\varepsilon,\varepsilon)$. We then refine this result by establishing a limit theorem for the hitting-time distributions of $(x-\varepsilon,x+\varepsilon)$ with arbitrary $x\in\mathbb{R}$.

#### Article information

Source
Ann. Probab., Volume 41, Number 2 (2013), 619-635.

Dates
First available in Project Euclid: 8 March 2013

https://projecteuclid.org/euclid.aop/1362750936

Digital Object Identifier
doi:10.1214/11-AOP698

Mathematical Reviews number (MathSciNet)
MR3077520

Zentralblatt MATH identifier
1266.60084

#### Citation

Pène, Françoise; Saussol, Benoît; Zweimüller, Roland. Recurrence rates and hitting-time distributions for random walks on the line. Ann. Probab. 41 (2013), no. 2, 619--635. doi:10.1214/11-AOP698. https://projecteuclid.org/euclid.aop/1362750936

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