A relation between Chung's and Strassen's laws of the iterated logarithm

Research output: Article

43 Citations (Scopus)

Abstract

Let W(t) be a standard Wiener process and let f(x) be a function from the compact class in Strassen's law of the iterated logarithm. We investigate the lim inf behavior of the variable sup |W(xT)(2T loglog T)-1/2-f(x)|, 0≦x≦1 suitably normalized as T→∞. This extends Chung's result valid for f(x)≡0, stating that lim inf.[ sup |(2 T loglog T)-1/2W(xT)|(loglog T)-1]=π/4 a.s. T→∞ 0≦x≦1

Original languageEnglish
Pages (from-to)287-301
Number of pages15
JournalZeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete
Volume54
Issue number3
DOIs
Publication statusPublished - jan. 1980

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Law of the Iterated Logarithm
Wiener Process
Valid
Class
Standards
Wiener process

ASJC Scopus subject areas

  • Statistics and Probability
  • Analysis
  • Mathematics(all)

Cite this

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