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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
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
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
Linking options:
https://www.mathnet.ru/eng/tvp5459https://doi.org/10.4213/tvp5459 https://www.mathnet.ru/eng/tvp/v66/i2/p327
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Abstract page: | 524 | Full-text PDF : | 164 | References: | 54 | First page: | 39 |
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