Geodesic
An estimate of the tail of the destribution for normolized and self-normolized sums
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 5, Tome 294 (2002), pp. 77-87

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Some combinatorical inequality is derived. Using it, new estimates are proved for probabilities of large deviation of normalized and self-normalized sums of independent and dependent positive random values. As a consequence a right-hand estimate is derived for strong law of large numbers. 
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     author = {V. A. Egorov},
     title = {An estimate of the tail of the destribution for normolized and self-normolized sums},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {77--87},
     publisher = {mathdoc},
     volume = {294},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2002_294_a5/}
}
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V. A. Egorov. An estimate of the tail of the destribution for normolized and self-normolized sums. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 5, Tome 294 (2002), pp. 77-87. http://geodesic.mathdoc.fr/item/ZNSL_2002_294_a5/