Abstract:
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 ω2ω2 is given.
Citation:
L. V. Osipov, “On the probabilities of large deviations for sums of independent random vectors”, Teor. Veroyatnost. i Primenen., 23:3 (1978), 510–526; Theory Probab. Appl., 23:3 (1979), 490–506
\Bibitem{Osi78}
\by L.~V.~Osipov
\paper On the probabilities of large deviations for sums of independent random vectors
\jour Teor. Veroyatnost. i Primenen.
\yr 1978
\vol 23
\issue 3
\pages 510--526
\mathnet{http://mi.mathnet.ru/tvp3066}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=509726}
\zmath{https://zbmath.org/?q=an:0437.60005}
\transl
\jour Theory Probab. Appl.
\yr 1979
\vol 23
\issue 3
\pages 490--506
\crossref{https://doi.org/10.1137/1123059}
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https://www.mathnet.ru/eng/tvp3066
https://www.mathnet.ru/eng/tvp/v23/i3/p510
This publication is cited in the following 7 articles:
Aurelija Kasparavičiūtė, Theorems of Large Deviations for the Sums of a Random Number of Independent Random Variables, 2013
M. S. Ermakov, “On large deviations of type II error probabilities of Kolmogorov and omega-squared tests”, J. Math. Sci. (N. Y.), 128:1 (2005), 2538–2555
V. R. Fatalov, “Precise Laplace-type asymptotics for moderate deviations
of the distributions of sums of independent Banach-valued random
elements”, Theory Probab. Appl., 48:4 (2004), 642–663
V. I. Piterbarg, V. R. Fatalov, “The Laplace method for probability measures in Banach spaces”, Russian Math. Surveys, 50:6 (1995), 1151–1239
I. R. Bagdasarova, E. I. Ostrovskii, “Nonuniform exponential estimates for large deviations in Banach space”, Theory Probab. Appl., 40:3 (1995), 538–542
V. V. Yurinskii, “On the asymptotics of large deviations in a Hilbert space. I”, Theory Probab. Appl., 36:1 (1991), 99–114
L. V. Osipov, “Large deviation probabilities of sums of independent random vectors for certain classes of sets”, Math. Notes, 31:1 (1982), 75–79
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