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2020 Large deviations related to the law of the iterated logarithm for Itô diffusions
Stefan Gerhold, Christoph Gerstenecker
Electron. Commun. Probab. 25: 1-11 (2020). DOI: 10.1214/20-ECP297


When a Brownian motion is scaled according to the law of the iterated logarithm, its supremum converges to one as time tends to zero. Upper large deviations of the supremum process can be quantified by writing the problem in terms of hitting times and applying a result of Strassen (1967) on hitting time densities. We extend this to a small-time large deviations principle for the supremum of scaled Itô diffusions, using as our main tool a refinement of Strassen’s result due to Lerche (1986).


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Stefan Gerhold. Christoph Gerstenecker. "Large deviations related to the law of the iterated logarithm for Itô diffusions." Electron. Commun. Probab. 25 1 - 11, 2020.


Received: 12 March 2019; Accepted: 9 February 2020; Published: 2020
First available in Project Euclid: 18 February 2020

zbMATH: 1434.60088
Digital Object Identifier: 10.1214/20-ECP297

Primary: 60F10 , 60J60 , 60J65

Keywords: boundary crossings , Itô diffusion , Large Deviations Principle , Law of the iterated logarithm


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