Asymptotic expansions of large deviations for sums of nonidentically distributed random variables

Abstract

The work is designated for obtaining asymptotic expansions and determination of structures of the remainder terms that take into consideration large deviations both in Cramer zones and Linnik power zones for the distribution function of sums of independent nonidentically distributed random variables (r.v.). In this scheme of summation of r.v., the results are obtained first by mainly using the general lemma on large deviations considering asymptotic expansions for an arbitrary r.v. with regular behaviour of its cumulants. Asymptotic expansions in the Cramer zone for the distribution function of sums of identically distributed r.v. have been investigated by A. Bikelis, A. Zemaitis, S. Jaksevicius. Note that asymptotic expansions for large deviations were first obtained in the probability theory by J. Kubilius.