LIL type behavior of multivariate Lévy processes at zero

Einmahl, Uwe

doi:10.1090/tran/7805

LIL type behavior of multivariate Lévy processes at zero
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Trans. Amer. Math. Soc. 372 (2019), 6437-6464 Request permission

Abstract:

We study the almost sure behavior of suitably normalized multivariate Lévy processes as $t \downarrow 0.$ 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.

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