A note on the stability of the local time of a wiener process

Endre Csáki, Antónia Földes

Research output: Contribution to journalArticle

12 Citations (Scopus)

Abstract

Let L(a, t) be the local time of a Wiener process, and put A(t) = sup a≤g(t) L(a, t) L(0, t)-1. It is shown that if g(t)=t 1 2(log t)-1(log log t)-1 and lim t→∞ A(t)=0 a.s. when p > 2 and lim sum t→∞ A(t)=0 a.s. when p = 1. A similar result is proved for random g(t) depending on the maximum of the Wiener process. These results settle a problem posed by Csörgo{combining double acute accent} and Révész [7].

Original languageEnglish
Pages (from-to)203-213
Number of pages11
JournalStochastic Processes and their Applications
Volume25
Issue numberC
DOIs
Publication statusPublished - 1987

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Keywords

  • Wiener process
  • diffusion
  • local time

ASJC Scopus subject areas

  • Statistics and Probability
  • Modelling and Simulation
  • Applied Mathematics

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