LIL type behaviour of multivariate Levy processes at zero

Abstract

We study the almost sure behaviour of suitably normalised multivariate Levy processes as t goes to zero. Among other results we find necessary and sufficient conditions for a law of a very slowly varying function which includes a general law of the iterated logarithm in this setting. We also look at the corresponding cluster set problem.

revision: some smaller corrections and Theorem 2.4 has been split up into two theorems