Asymptotic expansions in local theorems for the maximum of sums of random variables with mean zero
type: Item
instance of: scholarly article
title: Asymptotic expansions in local theorems for the maximum of sums of random variables with mean zero
zbMATH Open document ID: 0562.60022
DOI: 10.1007/BF00973575
author: V. V. Naudzhyunene
published in: Lithuanian Mathematical Journal
publication date: 1983-01-01T00:00:00Z
review text: The author considers a sequence \(\{\xi_ j\}\) of independent identically distributed random variables with mean value zero, variance \(\sigma^ 2\), moments \(\alpha_{\nu}\) and absolute moments \(\beta_{\nu}\) of order \(\nu\). He forms the related random variables \(S_ n=\sum^{n}_{j=1}\xi_ j\), \(\bar S_ n=\max_{1\leq k\leq n}S_ k\), \(\bar Z_ n=\bar S_ n/\sigma \sqrt{n}\). For the density of \(\bar Z_ n\) he gets an asymptotic expansion in form of a polynomial.
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 60G50
zbMATH DE Number: 3895989
zbMATH Keywords: asymptotic expansion
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/bf00973575
OpenAlex ID: W1999375795
description: scientific article; zbMATH DE number 3895989