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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 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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Submitted on : Monday, March 18, 2013 - 10:18:23 AM
Last modification on : Monday, October 11, 2021 - 2:22:06 PM
Long-term archiving on: : Thursday, June 20, 2013 - 4:00:22 PM

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Françoise Pene, Benoit Saussol, Roland Zweimüller. Recurrence rates and hitting-time distributions for random walks on the line. Annals of Probability, Institute of Mathematical Statistics, 2013, 41 (2), pp.619-635. ⟨10.1214/11-AOP698⟩. ⟨hal-00465047v2⟩

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