Teoriya Veroyatnostei i ee Primeneniya
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor
Guidelines for authors
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS


Teor. Veroyatnost. i Primenen.:
Year:
Volume:
Issue:
Page:
Find




Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register

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 5 scientific papers (total in 5 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 (5)
References:
PDF
HTML
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
\Bibitem{Jan21}
\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
\mathnet{http://mi.mathnet.ru/tvp5459}
\crossref{https://doi.org/10.4213/tvp5459}
\mathscinet{https://mathscinet.ams.org/mathscinet-getitem?mr=4466376}
\zmath{https://zbmath.org/?q=an:1470.60099}
\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}
Linking options:
  • https://www.mathnet.ru/eng/tvp5459
  • https://doi.org/10.4213/tvp5459
  • https://www.mathnet.ru/eng/tvp/v66/i2/p327
    • This publication is cited in the following 5 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
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2025