The law of the iterated logarithm for local time of a Lévy process

Abstract

Let {X t } be a one-dimensional Levy process with local timeL(t, x) andL *(t)=sup{L(t, x): x ∈ ℝ}. Under an assumption which is more general than being a symmetric stable process with index α>1, we obtain a LIL forL*(t). Also with an additional condition of symmetry, a LIL for range is proved.