Geodesic
A lower bound for large deviation probabilities of sum of independent random variables with finite variances
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 3, Tome 260 (1999), pp. 218-239 Cet article a éte moissonné depuis la source Math-Net.Ru

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Our objective is to obtain nonasymptotic estimates from below for large deviation probabilities of sum of independent random variables which are more general, sharp and natural than analogous estimates of other authors. 
@article{ZNSL_1999_260_a14,
     author = {L. V. Rozovskii},
     title = {A lower bound for large deviation probabilities of sum of independent random variables with finite variances},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {218--239},
     year = {1999},
     volume = {260},
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     url = {http://geodesic.mathdoc.fr/item/ZNSL_1999_260_a14/}
}
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L. V. Rozovskii. A lower bound for large deviation probabilities of sum of independent random variables with finite variances. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 3, Tome 260 (1999), pp. 218-239. http://geodesic.mathdoc.fr/item/ZNSL_1999_260_a14/