Kolmogorov's strong law of large numbers holds for pairwise uncorrelated random variables
Teoriâ veroâtnostej i ee primeneniâ, Tome 66 (2021) no. 2, pp. 327-341
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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.
@article{TVP_2021_66_2_a5,
author = {M. Janisch},
title = {Kolmogorov's strong law of large numbers holds for pairwise uncorrelated random variables},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {327--341},
publisher = {mathdoc},
volume = {66},
number = {2},
year = {2021},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_2021_66_2_a5/}
}
TY - JOUR AU - M. Janisch TI - Kolmogorov's strong law of large numbers holds for pairwise uncorrelated random variables JO - Teoriâ veroâtnostej i ee primeneniâ PY - 2021 SP - 327 EP - 341 VL - 66 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TVP_2021_66_2_a5/ LA - ru ID - TVP_2021_66_2_a5 ER -
M. Janisch. Kolmogorov's strong law of large numbers holds for pairwise uncorrelated random variables. Teoriâ veroâtnostej i ee primeneniâ, Tome 66 (2021) no. 2, pp. 327-341. http://geodesic.mathdoc.fr/item/TVP_2021_66_2_a5/