Large deviations and the Strassen theorem in Hölder norm

P. Baldi, G. Ben Arous, G. Kerkyacharian

Research output: Contribution to journalArticle

Abstract

We prove that Schilder's theorem, giving large deviations estimates for the Brownian motion multiplied by a small parameter, still holds with the sup-norm replaced by any Hölder norm with exponentα < 1 2. We produce examples which show that this is effectively a stronger result and, as an application, we prove Strassen's Iterated Logarithm Law in these stronger topologies.

Original languageEnglish (US)
Pages (from-to)171-180
Number of pages10
JournalStochastic Processes and their Applications
Volume42
Issue number1
DOIs
StatePublished - Aug 1992

Keywords

  • iterated logarithm law
  • large deviations

ASJC Scopus subject areas

  • Statistics and Probability
  • Modeling and Simulation
  • Applied Mathematics

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