Acta Mathematica Hungarica
Volume/Issue:
Volume 129: Issue 1-2
On the strong law of large numbers for delayed sums and random fields
Authors:
A. Gut Department of Mathematics, Uppsala University, Box 480, SE-751 06 Uppsala, Sweden

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U. Stadtmüller Department of Number Theory and Probability Theory, Ulm University, D-89069 Ulm, Germany

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Pages:
182–203
Online Publication Date:
29 May 2010
Publication Date:
01 Oct 2010
Article Category:
Research Article
DOI:
https://doi.org/10.1007/s10474-010-9272-x
Keywords:
delayed sums; window; slowly varying function; strong law of large numbers; random field; de Bruijn conjugate; primary 60F15, 60G50; secondary 60G70
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Abstract  

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 nα for 0 < α < 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.

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Cover Acta Mathematica Hungarica
Acta Mathematica Hungarica
Print ISSN:
0236-5294
Online ISSN:
1588-2632

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Acta Mathematica Hungarica
Language English
Size B5
Year of
Foundation		 1950
Volumes
per Year		 3
Issues
per Year		 6
Founder Magyar Tudományos Akadémia  
Founder's
Address		 H-1051 Budapest, Hungary, Széchenyi István tér 9.
Publisher Akadémiai Kiadó
Springer Nature Switzerland AG
Publisher's
Address		 H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
CH-6330 Cham, Switzerland Gewerbestrasse 11.
Responsible
Publisher		 Chief Executive Officer, Akadémiai Kiadó
ISSN 0236-5294 (Print)
ISSN 1588-2632 (Online)

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