Geodesic
The law of the iterated logarithm and probabilities of moderate deviations of sums of dependent random variables
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 27, Tome 474 (2018), pp. 195-198
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Sufficient conditions are found for the applicability of a classical law of the iterated logarithm to sequences of random variables without conditions of independence and the existence of any moments. 
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V. V. Petrov. The law of the iterated logarithm and probabilities of moderate deviations of sums of dependent random variables. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 27, Tome 474 (2018), pp. 195-198. http://geodesic.mathdoc.fr/item/ZNSL_2018_474_a13/

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

[2] V. V. Petrov, “O zakone povtornogo logarifma dlya posledovatelnosti nezavisimykh sluchainykh velichin s konechnymi dispersiyami”, Zap. nauchn. semin. POMI, 278, 2001, 182–186 | Zbl

[3] H. Rubin, J. Sethuraman, “Probabilities of moderate deviations”, Sankhya A, 27:2–4 (1965), 325–346 | MR | Zbl

[4] J. Sethuraman, “Probabilities of deviations”, Essays in probability and statistics, eds. R. C. Bose et al., Univ. North Carolina Press, Chapel Hill, 1970, 655–672 | MR

[5] V. V. Petrov, “O veroyatnostyakh umerennykh uklonenii”, Zap. nauchn. semin. POMI, 260, 1999, 214–217 | Zbl