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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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Preprints, Working Papers, ...
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https://hal.univ-brest.fr/hal-00465047
Contributor : Benoit Saussol Connect in order to contact the contributor
Submitted on : Thursday, March 18, 2010 - 4:59:26 PM
Last modification on : Monday, October 11, 2021 - 2:22:07 PM
Long-term archiving on: : Tuesday, June 22, 2010 - 10:37:43 AM

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  • HAL Id : hal-00465047, version 1
  • ARXIV : 1003.5073

Citation

Françoise Pene, Benoit Saussol, Roland Zweimüller. Recurrence rates and hitting-time distributions for random walks on the line. 2010. ⟨hal-00465047v1⟩

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