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Teoriya Veroyatnostei i ee Primeneniya, 2021, Volume 66, Issue 2, Pages 327–341
DOI: https://doi.org/10.4213/tvp5459 (Mi tvp5459) 		 
This article is cited in 4 scientific papers (total in 4 papers)

Kolmogorov's strong law of large numbers holds for pairwise uncorrelated random variables

M. Janisch

University of Zürich, Mathematics Department, Zürich, Switzerland
Full-text PDF (439 kB) Citations (4)
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DOI: https://doi.org/10.4213/tvp5459
Abstract: Using the approach of Etemadi for the strong law of large numbers [Z.Wahrsch. Verw. Gebiete, 55 (1981), pp. 119–122] and its elaboration by Csörgő, Tandori, and Totik [Acta Math.Hungar., 42 (1983), pp. 319–330], we give weaker conditions under which the strong law of large numbers still holds, namely for pairwise uncorrelated (and also for “quasi-uncorrelated”) random variables. We focus, in particular, on random variables which are not identically distributed. Our approach leads to another simple proof of the classical strong law of large numbers.
Keywords: strong law of large numbers, Kolmogorov condition, Etemadi theorem, pairwise uncorrelated random variables, quasi-uncorrelated random variables.
Received: 23.11.2020
Accepted: 25.11.2020
English version:
Theory of Probability and its Applications, 2021, Volume 66, Issue 2, Pages 263–275
DOI: https://doi.org/10.1137/S0040585X97T990381
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: M. Janisch, “Kolmogorov's strong law of large numbers holds for pairwise uncorrelated random variables”, Teor. Veroyatnost. i Primenen., 66:2 (2021), 327–341; Theory Probab. Appl., 66:2 (2021), 263–275
Citation in format AMSBIB
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\by M.~Janisch
\paper Kolmogorov's strong law of large numbers holds for pairwise uncorrelated random variables
\jour Teor. Veroyatnost. i Primenen.
\yr 2021
\vol 66
\issue 2
\pages 327--341
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\crossref{https://doi.org/10.4213/tvp5459}
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\transl
\jour Theory Probab. Appl.
\yr 2021
\vol 66
\issue 2
\pages 263--275
\crossref{https://doi.org/10.1137/S0040585X97T990381}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85120767566}
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  • https://www.mathnet.ru/eng/tvp/v66/i2/p327
    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теория вероятностей и ее применения Theory of Probability and its Applications
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