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Complete convergence for arrays and the law of the single logarithm
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
Ulm Univ, Dept Number Theory & Probabil Theory, D-89069 Ulm, Germany..
2017 (English)In: Bulletin of the Australian Mathematical Society, ISSN 0004-9727, E-ISSN 1755-1633, Vol. 96, no 2, 333-344 p.Article in journal (Refereed) Published
Abstract [en]

The present paper is devoted to complete convergence and the strong law of large numbers under moment conditions near those of the law of the single logarithm (LSL) for independent and identically distributed arrays. More precisely, we investigate limit theorems under moment conditions which are stronger than 2p for any p < 2, in which case we know that there is almost sure convergence to 0, and weaker than E X-4 = (log(+) vertical bar X vertical bar)(2) < infinity, in which case the LSL holds.

Place, publisher, year, edition, pages
CAMBRIDGE UNIV PRESS , 2017. Vol. 96, no 2, 333-344 p.
Keyword [en]
arrays, row-wise independence, independent and identically distributed, the law of the iterated logarithm, complete convergence, the strong law of large numbers, Borel-Cantelli lemmas, exponential bounds
National Category
Mathematics
Identifiers
URN: urn:nbn:se:uu:diva-337118DOI: 10.1017/S0004972717000582ISI: 000411403100018OAI: oai:DiVA.org:uu-337118DiVA: diva2:1168258
Available from: 2017-12-20 Created: 2017-12-20 Last updated: 2017-12-20Bibliographically approved

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Gut, Allan

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