Rosenthal type inequalities for \(B\)-valued strong mixing random fields and their applications
type: Item
instance of: scholarly article
title: Rosenthal type inequalities for \(B\)-valued strong mixing random fields and their applications
zbMATH Open document ID: 0916.60007
DOI: 10.1007/BF02901956
published in: Science in China. Series A
publication date: 1999-07-12T00:00:00Z
review text: The main result of the paper is a Rosenthal-type inequality for the partial sums of a strongly mixing random field with values in a Banach space \(B\). The notion of mixing is based on a maximal correlation coefficient where the correlations are taken from random variables with values in \(B\) and in its dual space \(B^\star\), respectively. \(B\) must be of Rademacher type \(p\). Furthermore either \(B^\star\) must have the Radon-Nikodym property or \(B\) has to be reflexive. Some applications on the weak law of large numbers for \(B\)-valued mixing sequences and on the Marcinkiewicz-Zygmund laws for \(B\)-valued mixing fields are given.
reviewed by: Dirk Tasche
Mathematics Subject Classification ID: 60B12
Mathematics Subject Classification ID: 60G60
zbMATH DE Number: 1207232
zbMATH Keywords: moment inequality
zbMATH Keywords: mixing
zbMATH Keywords: random field
zbMATH Keywords: law of large numbers
author: Lixin Zhang
MaRDI profile type: Publication
cites work: On the spectral density and asymptotic normality of weakly dependent random fields
cites work: Three theorems on \(\rho^*\)-mixing random fields
cites work: A CLT for the periodograms of a \(p\)-mixing random field
cites work: Q4169288
cites work: Moment Conditions for Almost Sure Convergence of Weakly Correlated Random Variables
cites work: Q3997990
cites work: Q3948379
full work available at URL: https://doi.org/10.1007/bf02901956
OpenAlex ID: W2015073462
description: scientific article; zbMATH DE number 1207232