On convergences of probability measures in different Prohorov-type metrics
type: Item
instance of: scholarly article
title: On convergences of probability measures in different Prohorov-type metrics
zbMATH Open document ID: 0951.60006
DOI: 10.1016/S0167-7152(99)00123-6
author: Ornella Arcudi
published in: Statistics \& Probability Letters
publication date: 2000-12-18T00:00:00Z
review text: The author investigates a `uniform approximation property' of sequences of probability measures which was used in a previous paper of the author to establish a conditional convergence theorem of the form \(E(Z\mid X_n) \to E(Z\mid X)\) for some Skorokhod representation \(X_n\) of \(P_n\), \(X\) of \(P\). It is shown that the uniform approximation property together with convergence in the Prokhorov metric (i.e. weak convergence) implies convergence in the minimal \(L^\infty\)-metric (denoted \(\pi_\infty\)). Under some weaker form of uniform approximation equivalence holds.
Mathematics Subject Classification ID: 60B10
zbMATH DE Number: 1420541
zbMATH Keywords: weak convergence
zbMATH Keywords: Prokhorov-type metrics
MaRDI profile type: Publication
cites work: Convergence of conditional expectations given the random variables of a Skorohod representation
cites work: Q3216028
cites work: Q3999495
cites work: Uniformities for the convergence in law and in probability
description: scientific article; zbMATH DE number 1420541