LIL type behavior of multivariate Lévy processes at zero
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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.References
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Additional Information
- Uwe Einmahl
- Affiliation: Department of Mathematics, Vrije Universiteit Brussel, Pleinlaan 2, 1050 Brussels, Belgium
- Email: ueinmahl@vub.be
- Received by editor(s): July 10, 2018
- Received by editor(s) in revised form: January 8, 2019
- Published electronically: March 26, 2019
- © Copyright 2019 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 372 (2019), 6437-6464
- MSC (2010): Primary 60F15; Secondary 60G51
- DOI: https://doi.org/10.1090/tran/7805
- MathSciNet review: 4024527