Geodesic
On the probabilities of large deviations for sums of independent random vectors
Teoriâ veroâtnostej i ee primeneniâ, Tome 23 (1978) no. 3, pp. 510-526 Cet article a éte moissonné depuis la source Math-Net.Ru

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We obtain an asymptotic formula for the probabilities of large deviations for sums of independent Hilbert-space-valued random vectors. As a consequence a result on the probabilities of large deviations for the statictics $\omega^2$ is given. 
@article{TVP_1978_23_3_a2,
     author = {L. V. Osipov},
     title = {On the probabilities of large deviations for sums of independent random vectors},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {510--526},
     year = {1978},
     volume = {23},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1978_23_3_a2/}
}
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L. V. Osipov. On the probabilities of large deviations for sums of independent random vectors. Teoriâ veroâtnostej i ee primeneniâ, Tome 23 (1978) no. 3, pp. 510-526. http://geodesic.mathdoc.fr/item/TVP_1978_23_3_a2/