Geodesic
Large deviation probabilities for some classes of distributions, satisfying the Cramer condition
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 6, Tome 298 (2003), pp. 161-185

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In the note limit theorems on large deviations of sum $X_1+\cdots+X_n$ of i.i.d. random variables under the assumption $\mathbf E X^2_1\,e^{\la X_1}\infty $ for some $\lambda>0$ are studied. 
@article{ZNSL_2003_298_a10,
     author = {L. V. Rozovskii},
     title = {Large deviation probabilities for some classes of distributions, satisfying the {Cramer} condition},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {161--185},
     publisher = {mathdoc},
     volume = {298},
     year = {2003},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2003_298_a10/}
}
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L. V. Rozovskii. Large deviation probabilities for some classes of distributions, satisfying the Cramer condition. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 6, Tome 298 (2003), pp. 161-185. http://geodesic.mathdoc.fr/item/ZNSL_2003_298_a10/