On the convergence of weighted sums of \(L_q\)-mixingale arrays
type: Item
instance of: scholarly article
title: On the convergence of weighted sums of \(L_q\)-mixingale arrays
zbMATH Open document ID: 0940.60029
DOI: 10.1023/A:1026445923796
author: Shixin Gan
published in: Acta Mathematica Hungarica
publication date: 2000-02-21T00:00:00Z
review text: A sequence of random variables \(\{U_n, n\geq 1\}\) is said to converge completely to a constant \(a\) if \(\sum_{n\geq 1} P(|U_n-a|\geq \varepsilon)<\infty\) for each \(\varepsilon>0\). Generalizing McLeish's concept of \(L_2\)-mixingale sequences the author introduces \(L_q\)-mixingale sequences and proves complete convergence, \(L_q\)-convergence and convergence in probability of weighted sums of triangular arrays of \(L_q\)-mixingales. An essential point in proving the results consists in applying a Bernstein-type inequality for bounded martingale difference sequences.
Mathematics Subject Classification ID: 60F15
Mathematics Subject Classification ID: 60F10
Mathematics Subject Classification ID: 60F25
Mathematics Subject Classification ID: 60G42
zbMATH DE Number: 1404421
zbMATH Keywords: complete convergence
zbMATH Keywords: \(L_q\)-mixingale
zbMATH Keywords: martingale difference sequence
zbMATH Keywords: triangular array
zbMATH Keywords: Bernstein's inequality
reviewed by: Lothar Heinrich
MaRDI profile type: Publication
full work available at URL: a:1026445923796
OpenAlex ID: W1717560477
description: scientific article; zbMATH DE number 1404421