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On the strong law of large numbers for delayed sums and random fields
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Mathematical Statistics.
2010 (English)In: Acta Mathematica Hungarica, ISSN 0236-5294, E-ISSN 1588-2632, Vol. 129, no 1-2, 182-203 p.Article in journal (Refereed) Published
Abstract [en]

A paper by Chow [3] contains (i.a.) a strong law for delayed sums, such that the length of the edge of the nth window equals n (alpha) for 0 < alpha < 1. In this paper we consider the kind of intermediate case when edges grow like n=L(n), where L is slowly varying at infinity, thus at a higher rate than any power less than one, but not quite at a linear rate. The typical example one should have in mind is L(n) = log n. The main focus of the present paper is on random field versions of such strong laws.

Place, publisher, year, edition, pages
2010. Vol. 129, no 1-2, 182-203 p.
Keyword [en]
delayed sums, window, slowly varying function, strong law of large numbers, random field, de Bruijn conjugate
National Category
URN: urn:nbn:se:uu:diva-134654DOI: 10.1007/s10474-010-9272-xISI: 000282167700012OAI: oai:DiVA.org:uu-134654DiVA: diva2:373793
Available from: 2010-12-01 Created: 2010-11-30 Last updated: 2011-03-01Bibliographically approved

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