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

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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. 
@article{ZNSL_2019_486_a13,
     author = {V. V. Petrov},
     title = {On the law of the iterated logarithm for sums of dependent random variables},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {229--232},
     publisher = {mathdoc},
     volume = {486},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2019_486_a13/}
}
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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/