Chung's Law and the Csáki Function

Natalia Gorn, Mikhail Lifshits

Research output

14 Citations (Scopus)

Abstract

We have found the limit ℒh = lim inf (log2 T)2/3 T → ∞ ∥W(T·)/(2T log2 T)1/2 - h∥ for a Wiener process W and a class of twice weakly differentiable functions h ∈ C[0, 1], thus solving the problem of the convergence rate in Chung's functional law for the so-called "slowest points". Our description is closely related to an interesting functional emerging from a large deviation problem for the Wiener process in a strip.

Original languageEnglish
Pages (from-to)399-420
Number of pages22
JournalJournal of Theoretical Probability
Volume12
Issue number2
DOIs
Publication statusPublished - 1 Jan 1999

Scopus subject areas

  • Statistics and Probability
  • Mathematics(all)
  • Statistics, Probability and Uncertainty

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