Geodesic
On the growth of sums of non-negative random variables
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 7, Tome 311 (2004), pp. 237-241

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Almost sure estimates of the growth of sums of non-negative random variables are established. A generalization of author's result on the growth of sums of the indicators of arbitrary events is obtained. 
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     author = {V. V. Petrov},
     title = {On the growth of sums of non-negative random variables},
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     url = {http://geodesic.mathdoc.fr/item/ZNSL_2004_311_a13/}
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V. V. Petrov. On the growth of sums of non-negative random variables. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 7, Tome 311 (2004), pp. 237-241. http://geodesic.mathdoc.fr/item/ZNSL_2004_311_a13/