Moment inequalities and complete moment convergence
type: Item
instance of: scholarly article
title: Moment inequalities and complete moment convergence
zbMATH Open document ID: 1180.60019
DOI: 10.1155/2009/271265
author: Soo Hak Sung
published in: Journal of Inequalities and Applications
publication date: 2009-11-03T00:00:00Z
full work available at URL: https://eudml.org/doc/117788
review text: Let \(\{Y_i\), \(1\leq i\leq n\}\) and \(\{Z_i\), \(1\leq i\leq n\}\) be sequences of random variables. For any \(\varepsilon> 0\) and \(a> 0\), bounds for \[ E\Biggl(\Biggl| \sum^n_{i=1} (Y_i+ Z_i)\Biggr|-\varepsilon a\Biggr)^+ \] and \[ E\Biggl(\max_{1\leq k\leq n}\Biggl|\sum^k_{i= 1} (Y_i+ Z_i)\Biggr|-\varepsilon a\Biggr)^+ \] are obtained. From these results, we establish general methods for obtaining the complete moment convergence. The results of \textit{Y. S. Chow} [Bull. Inst. Math., Acad. Sin. 16, No.~3, 177--201 (1988; Zbl 0655.60028)], \textit{M.-H. Zhu} [Discrete Dyn. Nat. Soc. 2007, Article ID 74296 (2007; Zbl 1181.60044)], and \textit{Y.-F. Wu} and \textit{D. Zhu} [J. Korean Stat. Soc., in press (2009)] are generalized and extended from independent (or dependent) random variables to random variables satisfying some mild conditions. Some applications to dependent random variables are discussed.
reviewed by: Allan Gut
Mathematics Subject Classification ID: 60E15
zbMATH DE Number: 5624530
Wikidata QID: Q59220002
MaRDI profile type: Publication
OpenAlex ID: W2122658226
cites work: Q5766606
cites work: On the subspaces of \(L^p\) \((p > 2)\) spanned by sequences of independent random variables
cites work: A comparison theorem on moment inequalities between negatively associated and independent random variables
cites work: Rosenthal's type inequalities for negatively orthant dependent random variables
cites work: Q3476066
cites work: Maximal inequalities for partial sums of \(\rho\)-mixing sequences
cites work: Maximal inequalities and an invariance principle for a class of weakly dependent random variables
cites work: Complete Convergence and the Law of Large Numbers
cites work: On a Theorem of Hsu and Robbins
cites work: Convergence Rates in the Law of Large Numbers
cites work: Q3802321
cites work: Convergence properties of partial sums for arrays of rowwise negatively orthant dependent random variables
description: scientific article; zbMATH DE number 5624530