Geodesic
Estimates of Berry--Esseen type for probabilities of large deviations under violation of Cram\'er condition
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 6 (2009), pp. 191-198

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Two-sided estimates for probabilities of large deviations for sums of independent random variables with finite variances are obtained. All asymptotics of the probabilities are described in terms of deviation function $\Lambda(x,y)$ of a sum of truncated random variables. All error terms are explicitly estimated by a modified Lyapunov ratio $L(H(x),y)$.
Keywords: probabilities of large deviations, deviation function, Lyapunov ratio. 
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     author = {A. I. Sakhanenko},
     title = {Estimates of {Berry--Esseen} type for probabilities of large deviations under violation of {Cram\'er} condition},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {191--198},
     publisher = {mathdoc},
     volume = {6},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2009_6_a9/}
}
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A. I. Sakhanenko. Estimates of Berry--Esseen type for probabilities of large deviations under violation of Cram\'er condition. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 6 (2009), pp. 191-198. http://geodesic.mathdoc.fr/item/SEMR_2009_6_a9/