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Gnedenko, B. V., and A. N. Kolmogorov: Limit distributions for sums of independent random variables. Moscow-Leningrad: Gostekhizdat, 1949 (in Russian). English translation: Cambridge/Mass.: Addison-Wesley, 1954.
Berry, A. C.: The accuracy of the Gaussian approximation to the sums of independent variates. Trans. Amer. math. Soc. 49, 122–136 (1941).
Zolotarev, V. M.: On the closeness of the distributions of the two sums of independent random variables. Teor. Verojatn. Primen. 10, 519–526 (1965) (in Russian).
Cramèr, H.: Sur un nouveau théoréme limite de la théorie des probabilités. Actual. Sci. et ind. Nr. 736. Paris 1938.
Petrov, V. V.: Generalization of the limit theorem of Cramèr. Uspekhi Mat. Nauk. 9, 195–202 (1954).
—: Extension of the limit theorem of Cramèr to not equally distributed independent variables. Vestnit Leningrad Univ., Ser. Mat., Mekh. Astron. 8, 13–25 (1953) (inRussian).
Richter, W.: Local limit theorems for large deviations. Teor. Verojatn. Primen. 2, 214–229 (1957) (in Russian).
Statulevičius, V. A.: Limiting theorems and their sharpenings for additive random functions and sums of weakly dependent random functions and sums of weakly dependent random variables. Trans. Third Prague Conf. Information Theory, Statistics Decision Functions; Random Processes, 683–687, Prague 1964 (in Russian).
Leonov, V. P.: Some applications of older semiinvariants to the theory of stationary random processes, Moscow: Nauka 1964 (in Russian).
Esscher, F.: On approximate computation of distribution functions, when the corresponding characteristic functions are known. Skand. Aktuarietidskr. 1–2, 78–86 (1963).
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Statulevičius, V.A. On large deviations. Z. Wahrscheinlichkeitstheorie verw Gebiete 6, 133–144 (1966). https://doi.org/10.1007/BF00537136
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DOI: https://doi.org/10.1007/BF00537136