A random approximation of set valued càdlàg functions
type: Item
instance of: scholarly article
title: A random approximation of set valued càdlàg functions
zbMATH Open document ID: 1062.60006
author: Pedro Terán
author: Miguel López-Díaz
published in: Journal of Mathematical Analysis and Applications
publication date: 2004-11-23T00:00:00Z
review text: A càdlàg (acronym for the French term: continue à\ droite, limite à\ gauche) function is a function continuous on the right with left limits. ``In this paper we study the problem of estimating a càdlàg function \(f\) whose values are compact convex sets. For this purpose a random selection of points in the interval \([0,1]\) is considered and for each selected point \(x\), a random sample in \(f(x)\). On the basis of this a sequence of approximants \(f_{n,m}\) is constructed (where \(n\) and \(m\) are the respective sample sizes). Under general conditions, rates of convergence are obtained for Skorokhod's \(J_1\) topology, and in case of continuity of the estimated function also for the uniform one.''
reviewed by: Hsien-Kuei Hwang
Mathematics Subject Classification ID: 60D05
Mathematics Subject Classification ID: 41A99
zbMATH DE Number: 2117747
zbMATH Keywords: set-valued operators
zbMATH Keywords: convex hull
zbMATH Keywords: random approximations
MaRDI profile type: Publication
full work available at URL: j.jmaa.2004.05.020
OpenAlex ID: W1995932318
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DOI: 10.1016/J.JMAA.2004.05.020
description: scientific article; zbMATH DE number 2117747