Geodesic
On the law of iterated logarithm for sums of the independent finite variation random variables
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 2, Tome 244 (1997), pp. 257-270
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The objective of the note is to find the simple but rather general conditions giving the opportunity to extend the Kolmogorov theorem on the law of iterated logarithm to the case of unbounded summands with finite variations. The obtained results include both Kolmogorov's and the Hartman\;–\;Wintner theorems. 
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     author = {L. V. Rozovskii},
     title = {On the law of iterated logarithm for sums of the independent finite variation random variables},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {257--270},
     year = {1997},
     volume = {244},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1997_244_a17/}
}
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L. V. Rozovskii. On the law of iterated logarithm for sums of the independent finite variation random variables. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 2, Tome 244 (1997), pp. 257-270. http://geodesic.mathdoc.fr/item/ZNSL_1997_244_a17/