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Teoriya Veroyatnostei i ee Primeneniya, 2008, Volume 53, Issue 4, Pages 641–664
DOI: https://doi.org/10.4213/tvp2458 (Mi tvp2458) 		 
This article is cited in 1 scientific paper (total in 1 paper)

On Large Deviations of Sums of Independent Random Vectors on the Boundary and Outside of the Cramér Zone. II

A. A. Borovkov, A. A. Mogul'skii

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
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DOI: https://doi.org/10.4213/tvp2458
Abstract: 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, Cramér large deviation zone, superlarge deviations, integrolocal theorems.
Received: 06.04.2008
English version:
Theory of Probability and its Applications, 2009, Volume 53, Issue 4, Pages 573–593
DOI: https://doi.org/10.1137/S0040585X97983833
Bibliographic databases:
Language: Russian
Citation: 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”, Teor. Veroyatnost. i Primenen., 53:4 (2008), 641–664; Theory Probab. Appl., 53:4 (2009), 573–593
Citation in format AMSBIB
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    		Теория вероятностей и ее применения Theory of Probability and its Applications
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