Convergence of weighted sums and laws of large numbers in \(D([0,1]; E)\)
type: Item
instance of: scholarly article
title: Convergence of weighted sums and laws of large numbers in \(D([0,1]; E)\)
zbMATH Open document ID: 0837.60005
published in: Journal of Multivariate Analysis
publication date: 1996-05-20T00:00:00Z
review text: Let \(D\) be the space of functions which are right-continuous and have left limits. It is shown that convergence in the Skorokhod \(J_1\)- topology of a sequence \((x_n)\) in \(D\) does not imply convergence of a sequence \((\overline x_n)\) of averages. However, convergence of a sequence \((x_n)\) is shown to imply convergence of the sequence \((\overline x_n)\) of averages in the \(M_1\) and \(M_2\) topologies. Finally, a sequence of independent \(D\)-valued random variables is constructed to show that the strong laws of large numbers with respect to \(J_1\) and uniform topologies are nonequivalent.
Mathematics Subject Classification ID: 60B12
zbMATH DE Number: 769839
zbMATH Keywords: Skorokhod space
zbMATH Keywords: convergence
zbMATH Keywords: weighted sums
zbMATH Keywords: laws of large numbers
author: Ioana Schiopu Kratina
author: Peter Z. Daffer
reviewed by: Rimas Norvaiša
MaRDI profile type: Publication
full work available at URL: jmva.1995.1037
OpenAlex ID: W2043251270
DOI: 10.1006/JMVA.1995.1037
description: scientific article; zbMATH DE number 769839