Geodesic
On large deviations of a self-normalized
Teoriâ veroâtnostej i ee primeneniâ, Tome 49 (2004) no. 4, pp. 794-802

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In the present paper we deduce exponential bounds on the probabilities of large deviations of a self-normalized sum of independent random variables. Summands are not assumed to be identically distributed.
Keywords: Berry–Esseen bound, Lyapunov ratio, self-normalized sum, large deviations. 
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     author = {S. V. Nagaev},
     title = {On large deviations of a self-normalized},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {794--802},
     publisher = {mathdoc},
     volume = {49},
     number = {4},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2004_49_4_a11/}
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S. V. Nagaev. On large deviations of a self-normalized. Teoriâ veroâtnostej i ee primeneniâ, Tome 49 (2004) no. 4, pp. 794-802. http://geodesic.mathdoc.fr/item/TVP_2004_49_4_a11/