Small time Chung-type LIL for L\'{e}vy processes
Frank Aurzada, Leif Doering, Mladen Savov
TL;DR
This paper establishes Chung-type laws of the iterated logarithm for Lévy processes at small times, providing new tools to connect small deviation estimates with LIL results and deriving exotic norming functions in certain cases.
Contribution
It introduces methods to translate small deviation estimates into laws of the iterated logarithm for Lévy processes at zero, including cases with exotic norming functions.
Findings
Laws of the iterated logarithm for Lévy processes at small times are established.
Tools are developed to connect small deviation estimates with LIL results.
Exotic norming functions are derived in specific examples.
Abstract
We prove Chung-type laws of the iterated logarithm for general L\'{e}vy 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 L\'{e}vy processes at small times in many concrete examples. In some cases, exotic norming functions are derived.
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