Geodesic
On Large Deviations of Sums of Independent Random Vectors on the Boundary and Outside of the Cram\'er Zone.~II
Teoriâ veroâtnostej i ee primeneniâ, Tome 53 (2008) no. 4, pp. 641-664

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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, Cramér large deviation zone, integrolocal theorems.
Mots-clés : superlarge deviations 
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     title = {On {Large} {Deviations} of {Sums} of {Independent} {Random} {Vectors} on the {Boundary} and {Outside} of the {Cram\'er} {Zone.~II}},
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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 Cram\'er 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/