How big are the increments of the local time of a recurrent random walk?

E. Csáki, A. Földes

Research output: Contribution to journalArticle

12 Citations (Scopus)

Abstract

Let N(t) be the local time at zero (the number of returns to zero up to time t) of a recurrent random walk. Consider the largest increments over subintervals of length at {Mathematical expression} The almost sure behaviour of {Mathematical expression}is shown to be the same as the behaviour of the corresponding increments of the local time of a Wiener process provided at/log t→∞. In the case at=c log t an Erdo{combining double acute accent}s-Rényi type result is obtained.

Original languageEnglish
Pages (from-to)307-322
Number of pages16
JournalZeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
Volume65
Issue number2
DOIs
Publication statusPublished - Jun 1 1983

ASJC Scopus subject areas

  • Analysis
  • Statistics and Probability
  • Mathematics(all)

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