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Complete convergence for arrays and the law of the single logarithm
Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Tillämpad matematik och statistik.
Ulm Univ, Dept Number Theory & Probabil Theory, D-89069 Ulm, Germany..
2017 (engelsk)Inngår i: Bulletin of the Australian Mathematical Society, ISSN 0004-9727, E-ISSN 1755-1633, Vol. 96, nr 2, s. 333-344Artikkel i tidsskrift (Fagfellevurdert) 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.

sted, utgiver, år, opplag, sider
CAMBRIDGE UNIV PRESS , 2017. Vol. 96, nr 2, s. 333-344
Emneord [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
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URN: urn:nbn:se:uu:diva-337118DOI: 10.1017/S0004972717000582ISI: 000411403100018OAI: oai:DiVA.org:uu-337118DiVA, id: diva2:1168258
Tilgjengelig fra: 2017-12-20 Laget: 2017-12-20 Sist oppdatert: 2017-12-20bibliografisk kontrollert

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