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Strong laws for sequences in the vicinity of the LIL
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
Univ Ulm, Dept Number Theory & Probabil Theory, D-89069 Ulm, Germany..
2017 (English)In: Statistics and Probability Letters, ISSN 0167-7152, E-ISSN 1879-2103, Vol. 122, 63-72 p.Article in journal (Refereed) Published
Abstract [en]

The present paper is devoted to strong laws of large numbers under moment conditions near those of the law of the iterated logarithm (LIL) for i.i.d sequences. More precisely, we wish to investigate possible limit theorems under moment conditions which are stronger than p for any p < 2, in which case we know that there is a.s. convergence to 0, and weaker than E X-2 < infinity, in which case the LIL holds.

Place, publisher, year, edition, pages
2017. Vol. 122, 63-72 p.
Keyword [en]
Sums of independent, identically distributed random variables, The law of the iterated logarithm, The strong law of large numbers, Borel-Cantelli lemmas, Exponential bounds
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:uu:diva-316928DOI: 10.1016/j.spl.2016.10.027ISI: 000392785600009OAI: oai:DiVA.org:uu-316928DiVA: diva2:1079690
Available from: 2017-03-09 Created: 2017-03-09 Last updated: 2017-03-09Bibliographically approved

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