On the non-symmetrical problem of large deviations
Teoriâ veroâtnostej i ee primeneniâ, Tome 20 (1975) no. 1, pp. 58-68

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The problem of large deviations for sums of independent identically distributed variables is considered. The distribution of each summand is assumed to belong to the domain of attraction of a stable law, one of its tails satisfying well-known Cramer's condition.
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L. V. Kim; A. V. Nagaev. On the non-symmetrical problem of large deviations. Teoriâ veroâtnostej i ee primeneniâ, Tome 20 (1975) no. 1, pp. 58-68. http://geodesic.mathdoc.fr/item/TVP_1975_20_1_a4/