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On the LSL for Random Fields
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Mathematical Statistics.
2011 (English)In: Journal of theoretical probability, ISSN 0894-9840, E-ISSN 1572-9230, Vol. 24, no 2, 422-449 p.Article in journal (Refereed) Published
Abstract [en]

In some earlier work, we have considered extensions of Lai's (Ann. Probab. 2:432-440, 1974) law of the single logarithm for delayed sums to a multi-index setting with the same as well as different expansion rates in the various dimensions. A further generalization concerns window sizes that are regularly varying with index 1 (on the line). In the present paper, we establish multi-index versions of the latter as well as for some mixtures of expansion rates. In order to keep things within reasonable size, we confine ourselves to some special cases for the index set Z(+.)(2).

Place, publisher, year, edition, pages
2011. Vol. 24, no 2, 422-449 p.
Keyword [en]
Delayed sums, Window, Law of the iterated logarithm, Law of the single logarithm, Sums of i.i.d. random variables, Slowly varying function, Multidimensional indices, Random fields
National Category
Mathematics
Identifiers
URN: urn:nbn:se:uu:diva-153570DOI: 10.1007/s10959-009-0265-zISI: 000289853900007OAI: oai:DiVA.org:uu-153570DiVA: diva2:417189
Available from: 2011-05-16 Created: 2011-05-16 Last updated: 2017-12-11Bibliographically approved

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