Convergence of conditional expectations given the random variables of a Skorohod representation
type: Item
instance of: scholarly article
title: Convergence of conditional expectations given the random variables of a Skorohod representation
zbMATH Open document ID: 0957.60003
DOI: 10.1016/S0167-7152(98)00060-1
author: Ornella Arcudi
published in: Statistics \& Probability Letters
publication date: 2001-03-18T00:00:00Z
review text: It is shown that under some technical condition on probability distributions \(P_n\Rightarrow P\) the Skorokhod representations \(X_n, X\) have the following interesting property: For any \(L^2\) random variable \(Z\) on \([0,1]\) the conditional expectations \(E(Z\mid {\mathcal F}^{X_n})\) converge in \(L^2\) to \(E(Z\mid {\mathcal F}^X)\). The proof is carried out by a detailed analysis of Billingsley's original proof of the Skorokhod representation together with martingale convergence arguments and estimates of conditional expectations in terms of sub-sigma-algebras. In an example it is shown that some additional condition is necessary for the main theorem to hold.
Mathematics Subject Classification ID: 60B10
zbMATH DE Number: 1368756
zbMATH Keywords: weak convergence
zbMATH Keywords: conditional expectation
zbMATH Keywords: Skorokhod representation
reviewed by: Hans-Peter Scheffler
MaRDI profile type: Publication
cites work: Q3794956
cites work: Q3216028
cites work: Convergence in distribution of conditional expectations
cites work: Uniform inequalities for conditional expectations
description: scientific article; zbMATH DE number 1368756