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 - 1992

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Brownian movement
Large Deviations
Logarithm laws
Topology
Norm
Theorem
Small Parameter
Brownian motion
Exponent
Estimate
Large deviations

Keywords

  • iterated logarithm law
  • large deviations

ASJC Scopus subject areas

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

Cite this

Large deviations and the Strassen theorem in Hölder norm. / Baldi, P.; Ben Arous, G.; Kerkyacharian, G.

In: Stochastic Processes and their Applications, Vol. 42, No. 1, 1992, p. 171-180.

Research output: Contribution to journalArticle

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