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 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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     title = {On the law of the iterated logarithm without assumptions about the existence of moments},
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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/

[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