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MATHEMATICS
On probabilities of large deviations of combinatorial sums of independent random variables satisfying Linnik's condition
A. N. Frolov St. Petersburg State University, 7-9, Universitetskaya nab., St. Petersburg, 199034, Russian Federation
Abstract:
We derive new results on asymptotic behaviour for probabilities of large deviations of combinatorial sums of independent random variables satisfying Linnik's condition. We find zones in which these probabilities are equivalent to the tail of the standard normal law. The author earlier obtained such results under Bernstein's condition. The truncations method is applied in proofs of results.
Keywords:
probabilities of large deviations, combinatorial central limit theorem, combinatorial sums.
Received: 02.01.2023 Accepted: 16.02.2023
Citation:
A. N. Frolov, “On probabilities of large deviations of combinatorial sums of independent random variables satisfying Linnik's condition”, Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 10:3 (2023), 545–553
Linking options:
https://www.mathnet.ru/eng/vspua259 https://www.mathnet.ru/eng/vspua/v10/i3/p545
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