Geodesic
On Large Deviations of Sums of Independent Random Vectors on the Boundary and Outside of the Cramér Zone. II
Teoriâ veroâtnostej i ee primeneniâ, Tome 53 (2008) no. 4, pp. 641-664 Cet article a éte moissonné depuis la source Math-Net.Ru

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The present paper continues [A. A. Borovkov and A. A. Mogulskii, Theory Probab. Appl., 53 (2009), pp. 301–311] and is devoted to studying the asymptotics of the probability that a sum of independent random vectors falls into a small cube with a vertex at a point $x$ in the large deviation zone. This asymptotics is found in the multivariate case for a class of distributions regularly varying at infinity and for deviations well beyond the Cramér zone.
Keywords: deviation function, large deviations, irregular large deviations, integrolocal theorems.
Mots-clés : Cramér large deviation zone, superlarge deviations 
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A. A. Borovkov; A. A. Mogul'skii. On Large Deviations of Sums of Independent Random Vectors on the Boundary and Outside of the Cramér Zone. II. Teoriâ veroâtnostej i ee primeneniâ, Tome 53 (2008) no. 4, pp. 641-664. http://geodesic.mathdoc.fr/item/TVP_2008_53_4_a0/

[1] Borovkov A. A., Mogulskii A. A., “Veroyatnosti bolshikh uklonenii dlya summ nezavisimykh sluchainykh vektorov na granitse i vne kramerovskoi zony. I”, Teoriya veroyatn. i ee primen., 53:2 (2008), 336–344

[2] Borovkov A. A., Mogulskii A. A., Bolshie ukloneniya i proverka statisticheskikh gipotez, Nauka, Novosibirsk, 1992, 223 pp.

[3] Zaigraev O., Large-deviation Theorems for Sums of Independent and Identically Distributed Random Vectors, Universytet Mikolaja Kopernika, Torun, 2005, 187 pp.

[4] Borovkov A. A., Borovkov K. A., “O veroyatnostyakh bolshikh uklonenii dlya sluchainykh bluzhdanii. I. Raspredeleniya s pravilno menyayuschimisya khvostami”, Teor. veroyatn. i ee primen., 46:2 (2001), 209–232 | MR | Zbl

[5] Borovkov A. A., Borovkov K. A., Asimptoticheskii analiz sluchainykh bluzhdanii. I. Medlenno ubyvayuschie raspredeleniya skachkov, Nauka, M. (to appear)

[6] Stone C., “On local and ratio limit theorems”, Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, part 2, v. II, Univ. of California Press, Berkeley, 1966, 217–224 | MR

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

[8] Rokafellar R., Vypuklyi analiz, Mir, M., 1973, 469 pp.