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

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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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     author = {V. V. Petrov},
     title = {On the law of the iterated logarithm without assumptions about the existence of moments},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {208--210},
     publisher = {mathdoc},
     volume = {466},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2017_466_a13/}
}
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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/