Small time Chung-type LIL for Lévy processes

Frank Aurzada; Leif Döring; Mladen Savov

doi:10.3150/11-BEJ395

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Home > Journals > Bernoulli > Volume 19 > Issue 1 > Article

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

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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.

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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