Open Access
February 2013 Small time Chung-type LIL for Lévy processes
Frank Aurzada, Leif Döring, Mladen Savov
Bernoulli 19(1): 115-136 (February 2013). DOI: 10.3150/11-BEJ395

Abstract

We prove Chung-type laws of the iterated logarithm for general Lévy processes at zero. In particular, we provide tools to translate small deviation estimates directly into laws of the iterated logarithm.

This reveals laws of the iterated logarithm for Lévy processes at small times in many concrete examples. In some cases, exotic norming functions are derived.

Citation

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Frank Aurzada. Leif Döring. Mladen Savov. "Small time Chung-type LIL for Lévy processes." Bernoulli 19 (1) 115 - 136, February 2013. https://doi.org/10.3150/11-BEJ395

Information

Published: February 2013
First available in Project Euclid: 18 January 2013

zbMATH: 1270.60044
MathSciNet: MR3019488
Digital Object Identifier: 10.3150/11-BEJ395

Keywords: Law of the iterated logarithm , Lévy process , small ball problem , Small deviations

Rights: Copyright © 2013 Bernoulli Society for Mathematical Statistics and Probability

Vol.19 • No. 1 • February 2013
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