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An intermediate Baum-Katz theorem
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Mathematical Statistics.
2011 (English)In: Statistics and Probability Letters, ISSN 0167-7152, Vol. 81, no 10, 1486-1492 p.Article in journal (Refereed) Published
Abstract [en]

We extend the classical Hsu–Robbins–Erdős 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).

Place, publisher, year, edition, pages
2011. Vol. 81, no 10, 1486-1492 p.
Keyword [en]
Sums of i.i.d. random variables, Convergence rates, Law of large numbers, Almost exponential moments, Random fields
National Category
URN: urn:nbn:se:uu:diva-158144DOI: 10.1016/j.spl.2011.05.008ISI: 000293485100004OAI: oai:DiVA.org:uu-158144DiVA: diva2:438938
Available from: 2011-09-06 Created: 2011-09-01 Last updated: 2011-09-06Bibliographically approved

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