On probabilities of moderate deviations
type: Item
instance of: scholarly article
title: On probabilities of moderate deviations
zbMATH Open document ID: 0996.60033
DOI: 10.1023/A:1014537601882
published in: Journal of Mathematical Sciences (New York)
publication date: 2002-06-25T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 60F10
Mathematics Subject Classification ID: 60G50
zbMATH DE Number: 1759038
zbMATH Keywords: zones of moderate deviations
zbMATH Keywords: Lyapunov fraction
zbMATH Keywords: Esseen inequality
author: V. V. Petrov
reviewed by: Zdzisław Rychlik
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1759038