On asymptotic behaviour for probabilities of moderate deviations of combinatorial sums
DOI:
https://doi.org/10.21638/spbu01.2023.412Abstract
We investigate an asymptotic behaviour for probabilities of moderate deviations of combinatorial sums of independent random variables having moments of order p > 2. We find zones in which these probabilities are equivalent to the tail of the standard normal law. The width of the zone is a function from the logarithm of a combinatorial variant for Lyapunov’s ratio. The author earlier obtained similar results under Bernstein’s and Linnik’s conditions. The truncations method is used in proofs of the results.
Keywords:
probabilities of large deviations, probabilities of moderate deviations, combinatorial central limit theorem, combinatorial sums
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Articles of "Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy" are open access distributed under the terms of the License Agreement with Saint Petersburg State University, which permits to the authors unrestricted distribution and self-archiving free of charge.