On the \(L^ 1_{{\mathcal F}}\) convergence for conditional Amarts
type: Item
instance of: scholarly article
title: On the \(L^ 1_{{\mathcal F}}\) convergence for conditional Amarts
zbMATH Open document ID: 0649.60040
DOI: 10.1016/0047-259X(88)90075-9
published in: Journal of Multivariate Analysis
publication date: 1988-01-01T00:00:00Z
review text: In this note we develop the relation between another type of conditional convergence of a sequence of random variables. Moreover, we generalise the theorem of convergence in \(L^ 1\) for amarts. An interesting result is stated in Theorem 4: Every uniformly \({\mathcal F}\)-integrable conditional amart converges a.s. and in \(L^ 1_{{\mathcal F}}\).
Mathematics Subject Classification ID: 60F25
Mathematics Subject Classification ID: 60G48
Mathematics Subject Classification ID: 60G42
zbMATH DE Number: 4060431
zbMATH Keywords: semiamart
zbMATH Keywords: amart
zbMATH Keywords: conditional convergence of a sequence of random variables
zbMATH Keywords: conditional amart
author: Wieslaw Zieba
MaRDI profile type: Publication
cites work: Pointwise convergence in terms of expectations
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cites work: Amarts: A class of asymptotic martingales. A: Discrete parameter
cites work: Q4114574
cites work: Q3769700
cites work: A note on the convergence of sequences of conditional expectations of random variables
description: scientific article; zbMATH DE number 4060431