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

• Autores: Françoise Pène, Benoît Saussol, Roland Zweimüller
• Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 41, Nº. 2, 2013, págs. 619-635
• Idioma: inglés
• DOI: 10.1214/11-AOP698
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• Resumen

  • 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 ε→0, of the return time to (−ε,ε). We then refine this result by establishing a limit theorem for the hitting-time distributions of (x−ε,x+ε) with arbitrary x∈R.