Sharp tail distribution estimates for the supremum of a class of sums of i.i.d. random variables
type: Item
instance of: scholarly article
title: Sharp tail distribution estimates for the supremum of a class of sums of i.i.d. random variables
zbMATH Open document ID: 1343.60022
published in: Stochastic Processes and their Applications
publication date: 2015-12-08T00:00:00Z
review text: Consider a sequence of random variables \(f(\xi_1),\dots,f(\xi_n)\), where \(\xi_1,\dots,\xi_n\) are independent and identically distributed, and \(f(\xi_1)\) has zero mean and finite second moment. This paper establishes a sharp bound for the tail probability of the supremum of the normalized sums of \(f(\xi_1),\dots,f(\xi_n)\) under various conditions, which are discussed in detail in the paper. The usefulness of these results in the study of the uniform central limit theorem is illustrated in the paper.
reviewed by: Dongsheng Tu
Mathematics Subject Classification ID: 60F10
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 60G50
zbMATH DE Number: 6518038
zbMATH Keywords: i.i.d. random variables
zbMATH Keywords: sums
zbMATH Keywords: tail distribution
zbMATH Keywords: uniform central limit theorem
author: P. Major
MaRDI profile type: Publication
full work available at URL: j.spa.2015.07.017
OpenAlex ID: W1185089419
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DOI: 10.1016/J.SPA.2015.07.017
description: scientific article; zbMATH DE number 6518038