Geodesic
Superlarge deviations of a sum of independent random variables having a common absolutely continuous distribution under the Cram\'er condition
Teoriâ veroâtnostej i ee primeneniâ, Tome 48 (2003) no. 1, pp. 78-103

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This paper studies the asymptotic behavior of a density of a sum of independent identically distributed random variables with a common absolutely continuous distribution satisfying the right-hand Cramér condition. We prove that for a definite class of such distributions the well-known asymptotic representations in local and integral limit theorems are valid in the case of large deviations of arbitrarily high order.
Keywords: independent random variables, density function, large deviations, Cramér condition. 
@article{TVP_2003_48_1_a4,
     author = {L. V. Rozovskii},
     title = {Superlarge deviations of a sum of independent random variables having a common absolutely continuous distribution under the {Cram\'er} condition},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {78--103},
     publisher = {mathdoc},
     volume = {48},
     number = {1},
     year = {2003},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2003_48_1_a4/}
}
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L. V. Rozovskii. Superlarge deviations of a sum of independent random variables having a common absolutely continuous distribution under the Cram\'er condition. Teoriâ veroâtnostej i ee primeneniâ, Tome 48 (2003) no. 1, pp. 78-103. http://geodesic.mathdoc.fr/item/TVP_2003_48_1_a4/