Small time two-sided LIL behavior for Lévy processes at zero

Savov, M. (2009) Small time two-sided LIL behavior for Lévy processes at zero. Probability Theory and Related Fields, 144 (1-2). pp. 79-98. ISSN 1432-2064 doi: 10.1007/s00440-008-0142-1

Abstract/Summary

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.