Geodesic
Lower Bounds on Large Deviation Probabilities for Sums of Independent Random Variables
Teoriâ veroâtnostej i ee primeneniâ, Tome 46 (2001) no. 1, pp. 50-73

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This paper derives the lower estimates for large deviation probabilities for sums of independent random variables. The area of application of these estimates is described in terms of a Lyapunov ratio. The obtained estimates are compared with lower estimates obtained by Kolmogorov, Feller, Lenart, and Arkhangelskii.
Keywords: large deviations, method of conjugate distributions, independent random variables, Kolmogorov inequality, Berry–Esseen estimators, convolution of distribution functions, Bernstein condition, characteristic function.
Mots-clés : ratio 
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     author = {S. V. Nagaev},
     title = {Lower {Bounds} on {Large} {Deviation} {Probabilities} for {Sums} of {Independent} {Random} {Variables}},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {50--73},
     publisher = {mathdoc},
     volume = {46},
     number = {1},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2001_46_1_a2/}
}
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S. V. Nagaev. Lower Bounds on Large Deviation Probabilities for Sums of Independent Random Variables. Teoriâ veroâtnostej i ee primeneniâ, Tome 46 (2001) no. 1, pp. 50-73. http://geodesic.mathdoc.fr/item/TVP_2001_46_1_a2/