Small time Chung-type LIL for Lévy processes

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.

Published in at http://dx.doi.org/10.3150/11-BEJ395 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)

References in corpus (4)

• Small deviations for fractional stable processes
• Passage of Lévy Processes across Power Law Boundaries at Small Times
• Small deviations of general Lévy processes
• Shifted small deviations and Chung LIL for symmetric alpha-stable processes

Cited by in corpus (4)

• Laws of the iterated logarithm for symmetric jump processes
• A Note on the Multivariate CLT and Convergence of Levy Processes at Long and Short Times
• Intermittency in the small-time behavior of Lévy processes
• Conditions for a Lévy process to stay positive near 0, in probability