Some convergence theorem for random variables in a Hilbert space with application
type: Item
instance of: scholarly article
zbMATH Open document ID: 1306.60023
DOI: 10.5831/HMJ.2014.36.3.679
author: Kwang-Hee Han
published in: Honam Mathematical Journal
publication date: 2014-10-29T00:00:00Z
Mathematics Subject Classification ID: 60F17
Mathematics Subject Classification ID: 60B12
Mathematics Subject Classification ID: 60B11
zbMATH DE Number: 6362214
zbMATH Keywords: asymptotically negative dependence
zbMATH Keywords: convergence theorem
zbMATH Keywords: Hilbert space
zbMATH Keywords: linear process
zbMATH Keywords: linear bounded operator
zbMATH Keywords: almost sure convergence
zbMATH Keywords: Rosenthal type inequality
MaRDI profile type: Publication
title: Some convergence theorem for random variables in a Hilbert space with application
review text: In this paper, the notion of asymptotically negative dependence for random vectors with values in \({\mathbb R}^d, d\geq1\), is introduced and this notion is generalized to a Hilbert space. Moreover, conditions for almost sure convergence of negatively associated random vectors in a separable real Hilbert space \(H\) are obtained and this result is applied to a linear process generated by \(H\)-valued asymptotically negatively dependent random vectors.
reviewed by: Vakhtang V. Kvaratskhelia
description: scientific article; zbMATH DE number 6362214