Large deviations and the Strassen theorem in Hölder norm

P. Baldi; G. Ben Arous; G. Kerkyacharian

doi:10.1016/0304-4149(92)90033-M

Large deviations and the Strassen theorem in Hölder norm

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

Mathematics

Research output: Contribution to journal › Article › peer-review

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 language	English (US)
Pages (from-to)	171-180
Number of pages	10
Journal	Stochastic Processes and their Applications
Volume	42
Issue number	1
DOIs	https://doi.org/10.1016/0304-4149(92)90033-M
State	Published - Aug 1992

Keywords

iterated logarithm law
large deviations

ASJC Scopus subject areas

Statistics and Probability
Modeling and Simulation
Applied Mathematics

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10.1016/0304-4149(92)90033-M

Cite this

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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 H{\"o}lder 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.",

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AB - 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.

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Large deviations and the Strassen theorem in Hölder norm

Abstract

Keywords

ASJC Scopus subject areas

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