This article is cited in 1 paper

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.

UDC: 519.2

MSC: 60F05

Received: 02.01.2023
Accepted: 16.02.2023

DOI: 10.21638/spbu01.2023.308