An intermediate Baum-Katz theorem |
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Authors: | Allan Gut Ulrich Stadtmüller |
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Institution: | a Department of Mathematics, Uppsala University, Box 480, SE-75106 Uppsala, Swedenb Ulm University, Department of Number Theory and Probability Theory, D-89069 Ulm, Germany |
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Abstract: | We extend the classical Hsu-Robbins-Erd?s theorem to the case when all moments exist, but the moment generating function does not, viz., we assume that Eexp{(log+|X|)α}<∞ for some α>1. We also present multi-index versions of the same and of a related result due to Lanzinger in which the assumption is that Eexp{|X|α}<∞ for some α∈(0,1). |
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Keywords: | primary 60F15 60G50 60G60 secondary 60F05 |
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