Geodesic
On the law of the iterated logarithm for sums of dependent random variables
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 28, Tome 486 (2019), pp. 229-232 
V. V. Petrov. On the law of the iterated logarithm for sums of dependent random variables. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 28, Tome 486 (2019), pp. 229-232. http://geodesic.mathdoc.fr/item/ZNSL_2019_486_a13/
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     title = {On the law of the iterated logarithm for sums of dependent random variables},
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     url = {http://geodesic.mathdoc.fr/item/ZNSL_2019_486_a13/}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

Sufficient conditions are found for the applicability of the generalized law of the iterated logarithm for sums of dependent random variables in the case when the sequence of normalizing constants is not necessarily nondecreasing.

[1] V. V. Petrov, “O zakone povtornogo logarifma bez predpolozhenii o suschestvovanii momentov”, Zap. nauchn. semin. POMI, 466, 2017, 208–210

[2] A. Kolmogoroff, “Über das Gesetz des iterierten Logarithmus”, Math. Ann., 101 (1929), 126–135 | DOI | MR | Zbl

[3] V. V. Petrov, Limit Theorems of Probability Theory, Oxford University Press, Oxford–New York, 1995 | MR | Zbl

[4] W. Hoeffding, H. Robbins, “The central limit theorem for dependent random variables”, Duke Math., 15:3 (1948), 773–780 | DOI | MR | Zbl

[5] V. V. Petrov, “O zakone povtornogo logarifma dlya posledovatelnostei zavisimykh sluchainykh velichin”, Zap. nauchn. semin. POMI, 97, 1980, 186–194 | Zbl

[6] V. V. Petrov, “Posledovatelnosti $m$-ortogonalnykh sluchainykh velichin”, Zap. nauchn. semin. POMI, 119, 1982, 198–202 | Zbl

[7] V. V. Petrov, “O zakone povtornogo logarifma dlya posledovatelnostei zavisimykh sluchainykh velichin”, Vestnik SPbU, ser. 1 (Matematika), 2017, no. 1, 49–51