The small-time Chung-Wichura law for Levy processes with non-vanishing Brownian component

Boris Buchmann, Ross Maller

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Abstract

We give a small time functional version of Chung s other law of the iterated logarithm for Levy processes with non-vanishing Brownian component. This is an analogue of the other law of the iterated logarithm at large times for Levy processes and random walks with finite variance, as extended to a functional version by Wichura. As one of many possible applications, we mention a functional law for a two-sided passage time process.
Original languageEnglish
Pages (from-to)1 - 28
Number of pages28
JournalProbability Theory and Related Fields
VolumeE
Publication statusPublished - 2011

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