Geodesic
On the law of the iterated logarithm without assumptions about the existence of moments
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 26, Tome 466 (2017), pp. 208-210 
V. V. Petrov. On the law of the iterated logarithm without assumptions about the existence of moments. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 26, Tome 466 (2017), pp. 208-210. http://geodesic.mathdoc.fr/item/ZNSL_2017_466_a13/
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     title = {On the law of the iterated logarithm without assumptions about the existence of moments},
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     year = {2017},
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     url = {http://geodesic.mathdoc.fr/item/ZNSL_2017_466_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 random variables without conditions of independence and the existence of moments.

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

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