Geodesic
On the rate of convergence in the strong law of large numbers for non-negative random variables
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 24, Tome 454 (2016), pp. 183-194

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We study the rate of convergence in the strong law of large numbers for sequences of non-negative random variables without the independence assumption. We obtain conditions for which an analog of the Baum–Katz theorem holds. 
@article{ZNSL_2016_454_a10,
     author = {V. M. Korchevsky},
     title = {On the rate of convergence in the strong law of large numbers for non-negative random variables},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {183--194},
     publisher = {mathdoc},
     volume = {454},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2016_454_a10/}
}
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V. M. Korchevsky. On the rate of convergence in the strong law of large numbers for non-negative random variables. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 24, Tome 454 (2016), pp. 183-194. http://geodesic.mathdoc.fr/item/ZNSL_2016_454_a10/