Geodesic
Some limit theorems for large deviations of sums of independent random variables with a common distribution function from the domain of normal attraction of a stable distribution
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 29, Tome 495 (2020), pp. 250-266

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We examine certain questions, related to the convergence rate in the so-called “precise asymptotics”, when a limiting law is stable (including the normal one). In particular, the results obtained in Gut and Steinebach, (Ann. Univ. Sci. Budapest. Sect. Comput. 39:95–110, 2013) are generalized and refined. 
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     author = {L. V. Rozovsky},
     title = {Some limit theorems for large deviations of sums of independent random variables with a common distribution function from the domain of normal attraction of a stable distribution},
     journal = {Zapiski Nauchnykh Seminarov POMI},
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     url = {http://geodesic.mathdoc.fr/item/ZNSL_2020_495_a14/}
}
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L. V. Rozovsky. Some limit theorems for large deviations of sums of independent random variables with a common distribution function from the domain of normal attraction of a stable distribution. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 29, Tome 495 (2020), pp. 250-266. http://geodesic.mathdoc.fr/item/ZNSL_2020_495_a14/