Abstract
We wish to characterize when a Lévy process X t crosses boundaries b(t), in a two-sided sense, for small times t, where b(t) satisfies very mild conditions. An integral test is furnished for computing the value of sup t→0|X t |/b(t) = c. In some cases, we also specify a function b(t) in terms of the Lévy triplet, such that sup t→0 |X t |/b(t) = 1.
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Savov, M. Small time two-sided LIL behavior for Lévy processes at zero. Probab. Theory Relat. Fields 144, 79–98 (2009). https://doi.org/10.1007/s00440-008-0142-1
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DOI: https://doi.org/10.1007/s00440-008-0142-1