Geodesic
Superlarge deviations for sums of random variables with arithmetical super-exponential distributions
Matematičeskie trudy, Tome 11 (2008) no. 1, pp. 81-112 Cet article a éte moissonné depuis la source Math-Net.Ru

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Local limit theorems are obtained for superlarge deviations of sums $S(n)=\xi(1)+\dots+\xi(n)$ of independent identically distributed random variables having an arithmetical distribution with the right-hand tail decreasing faster that that of a Gaussian law. The distribution of $\xi$ has the form $\mathbb P(\xi=k)=e^{-k^\beta L(k)}$, where $\beta>2$, $k\in\mathbb Z$ ($\mathbb Z$ is the set of all integers), and $L(t)$ is a slowly varying function as $t\to\infty$ which satisfies some regularity conditions. These theorems describing an asymptotic behavior of the probabilities $\mathbb P\bigl(S(n)=k\bigr)$ as $k/n\to\infty$, complement the results on superlarge deviations in [1, 2]. 
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A. A. Mogulskiǐ; Ch. Pagma. Superlarge deviations for sums of random variables with arithmetical super-exponential distributions. Matematičeskie trudy, Tome 11 (2008) no. 1, pp. 81-112. http://geodesic.mathdoc.fr/item/MT_2008_11_1_a4/

[1] Borovkov A. A., Teoriya veroyatnostei, 3-e izd., Editorial URSS, M.; Izd-vo In-ta matematiki SO RAN, Novosibirsk, 1999

[2] Borovkov A. A., Mogulskii A. A., Bolshie ukloneniya i proverka statisticheskikh gipotez, Nauka, Novosibirsk, 1992 | Zbl

[3] Borovkov A. A., Mogulskii A. A., “Integro-lokalnye teoremy dlya summ nezavisimykh sluchainykh vektorov v skheme serii”, Mat. zametki, 79:4 (2006), 505–521 | MR | Zbl

[4] Borovkov A. A., Mogulskii A. A., “O bolshikh i sverkhbolshikh ukloneniyakh summ nezavisimykh sluchainykh vektorov pri vypolnenii usloviya Kramera. I”, Teoriya veroyatnostei i ee primeneniya, 51:2 (2006), 260–294 | MR

[5] Borovkov A. A., Mogulskii A. A., “O bolshikh i sverkhbolshikh ukloneniyakh summ nezavisimykh sluchainykh vektorov pri vypolnenii usloviya Kramera. II”, Teoriya veroyatnostei i ee primeneniya, 51:4 (2006), 641–673 | MR

[6] Borovkov A. A., Mogulskii A. A., “Predelnye teoremy dlya summ sluchainykh velichin s semieksponentsialnymi raspredeleniyami, deistvuyuschie na vsei osi”, Sib. mat. zhurn., 47:6 (2006), 1218–1257 | MR | Zbl

[7] Nagaev A. V., “Lokalnye teoremy s uchetom bolshikh uklonenii”, Predelnye teoremy i veroyatnostnye protsessy, Fan, Tashkent, 1967, 71–88 | MR

[8] Nagaev A. V., “Predelnye teoremy dlya odnoi skhemy serii”, Predelnye teoremy i veroyatnostnye protsessy, Fan, Tashkent, 1967, 43–70 | MR

[9] Seneta E., Pravilno menyayuschiesya funktsii, Nauka, M., 1985 | MR | Zbl