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Between the LIL and the LSL
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Mathematical Statistics. (Mathematical statistics)
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Mathematical Statistics. (Mathematical statistics)
2010 (English)In: Bernoulli, ISSN 1350-7265, Vol. 16, no 1, 1-22 p.Article in journal (Refereed) Published
Abstract [en]

In two earlier papers, two of the present authors (A.G. and U.S.) extended Lai's [Ann. Probab. 2 (1974) 432-440] law of the single logarithm for delayed sums to a multiindex setting in which the edges of the nth window grow like |n|α, or with different α's, where the α's belong to (0,1). In this paper, the edge of the nth window typically grows like n/log n, thus at a higher rate than any power less than one, but not quite at the LIL-rate.

Place, publisher, year, edition, pages
2010. Vol. 16, no 1, 1-22 p.
Keyword [en]
Delayed sums, Law of the iterated logarithm, Law of the single logarithm, Slowly varying function, Sums of i.i.d. random variables, Window
National Category
Mathematics
Identifiers
URN: urn:nbn:se:uu:diva-105909DOI: 10.3150/09-BEJ195ISI: 000275977500001OAI: oai:DiVA.org:uu-105909DiVA: diva2:222795
Available from: 2009-06-09 Created: 2009-06-09 Last updated: 2012-07-26Bibliographically approved

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Gut, AllanJonsson, Fredrik

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