Geodesic
Probabilities of large deviations in Banach spaces
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 4, Tome 278 (2001), pp. 86-111

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A theorem about the exact asymptotics of large derivatives of sums of independent random elements in a Banach space is proved. The results are a version of a Bentkus' and Rachkauskas' theorems. 
@article{ZNSL_2001_278_a4,
     author = {M. S. Ermakov},
     title = {Probabilities of large deviations in {Banach} spaces},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {86--111},
     publisher = {mathdoc},
     volume = {278},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2001_278_a4/}
}
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M. S. Ermakov. Probabilities of large deviations in Banach spaces. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 4, Tome 278 (2001), pp. 86-111. http://geodesic.mathdoc.fr/item/ZNSL_2001_278_a4/