2013•BernoulliOpen access

Small time Chung-type LIL for Lévy processes

Frank Aurzada, Leif Döring, Mladen Savov

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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Key concepts: Law of the iterated logarithm, Iterated logarithm, Mathematics, Logarithm, Type (biology), Iterated function, Natural logarithm, Zero (linguistics)