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March 2013 Recurrence rates and hitting-time distributions for random walks on the line
Françoise Pène, Benoît Saussol, Roland Zweimüller
Ann. Probab. 41(2): 619-635 (March 2013). DOI: 10.1214/11-AOP698

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} $.

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Françoise Pène. Benoît Saussol. Roland Zweimüller. "Recurrence rates and hitting-time distributions for random walks on the line." Ann. Probab. 41 (2) 619 - 635, March 2013. https://doi.org/10.1214/11-AOP698

Information

Published: March 2013
First available in Project Euclid: 8 March 2013

zbMATH: 1266.60084
MathSciNet: MR3077520
Digital Object Identifier: 10.1214/11-AOP698

Subjects:
Primary: 60E07 , 60F05 , 60G50

Keywords: hitting time , quantitative recurrence , Random walk , recurrence , stable distribution

Rights: Copyright © 2013 Institute of Mathematical Statistics

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Vol.41 • No. 2 • March 2013
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