On the Asymmetrical Problem of Large Deviations
L. V. Kim, A. V. Nagaev · Theory of Probability and Its Applications · 1975
Previous article Next article On the Asymmetrical Problem of Large DeviationsL. V. Kim and A. V. NagaevL. V. Kim and A. V. Nagaevhttps://doi.org/10.1137/1120005PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] V. M. Zolotarev, On a new viewpoint of limit theorems taking into account large deviations, Proc. Sixth All-Union Conf. Theory Prob. and Math. Statist. (Vilnius, 1960) (Russian), Gosudarstv. Izdat. Političesk. i Naučn. Lit. Litovsk. SSR, Vilnius, 1962, 43–47 MR0192539 Google Scholar[2] I. A. Ibragimov and , Yu. V. Linnik, Independent and stationary sequences of random variables, Wolters-Noordhoff Publishing, Groningen, 1971, 443– MR0322926 0219.60027 Google Scholar[3] C. C. Heyde, On large deviation probabilities in the case of attraction to a non-normal stable law, Sankhyā Ser. A, 30 (1968), 253–258 MR0240854 0182.22903 Google Scholar[4] A. Aleškjavičene, Limit theorems for large deviations, Litovsk. Mat. Sb., 2 (1962), 5–13, (In Russian.) MR0156375 Google Scholar[5] P. Vai˘tkus, Large deviations of sums of random variables in the case of a stable limit law, Litovsk. Mat. Sb., 12 (1972), 85–97, 233, (In Russian.) MR0319245 Google Scholar[6] V. V. Petrov, Sums of Independent Random Variables, Nauka, Moscow, 1972, (In Russian.) Google Scholar[7] I. S. Gradshtein and , I. M. Rishik, Tables of Integrals, Sums, Series and Products, Fizmatgiz, Moscow, 1962, (In Russian.) Google Scholar[8] Jean Bretagnolle and , Didier Dacunha-Castelle, Théorèmes limites à distance finie pour les marches aléatoires, Ann. Inst. H. Poincaré Sect. B (N.S.), 4 (1968), 25–73, Calcul des probabilités et statistique MR0235598 0164.47402 Google Scholar[9] A. V. Nagaev, Some remarks about multidimensional local limit theorems, Mat. Zametki, 14 (1973), 559–563, (In Russian.) MR0331480 0296.60018 Google Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Asymptotic and structural properties of special cases of the Wright function arising in probability theory25 July 2016 | Lithuanian Mathematical Journal, Vol. 56, No. 3 Cross Ref Asymptotic properties of stable densities and the asymmetric large deviation problemsStatistics & Probability Letters, Vol. 61, No. 4 Cross Ref Cramer Large Deviations when the Extreme Conjugate Distribution is Heavy-tailedA. V. Nagaev25 July 2006 | Theory of Probability & Its Applications, Vol. 43, No. 3AbstractPDF (380 KB)Probabilities of Large Deviations for Sums ofIndependent Random Variables with a Common Distribution Functionfrom the Domain of Attraction of an Asymmetric Stable LawL. V. Rozovskii17 February 2012 | Theory of Probability & Its Applications, Vol. 42, No. 3AbstractPDF (430 KB)On the Asymmetric Problem of Large Deviations When the Limit Law is StableA. V. Nagaev28 July 2006 | Theory of Probability & Its Applications, Vol. 28, No. 4AbstractPDF (713 KB) Volume 20, Issue 1| 1975Theory of Probability & Its Applications History Submitted:13 December 1973Published online:17 July 2006 InformationCopyright © 1975 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1120005Article page range:pp. 57-68ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics