On probabilities of moderate deviations (Q1603218)

The author investigates the asymptotic behaviour of the distribution of a sum of independent random variables in zones of moderate deviations. Sufficient conditions are presented, in terms of moments, for the normal convergence in these zones. The author uses a generalization of the Esseen inequality for the remainder term in the central limit theorem. This permits him to give a short proof of the normal convergence in zones of moderate deviations, formulated in terms of the generalized Lyapunov fractions.