A discrete stochastic Korovkin theorem
type: Item
instance of: scholarly article
title: A discrete stochastic Korovkin theorem
zbMATH Open document ID: 0796.60038
DOI: 10.1155/S016117129100090X
author: George A. Anastassiou
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 1992-06-28T00:00:00Z
full work available at URL: https://eudml.org/doc/46979
review text: Given a probability space \((\Omega,{\mathcal F},P)\) and a countable set \(T\), denote by \(B_ 0(T)\) the vector space of all stochastic processes \(X(T,\omega)\) with real state space and index set \(T\) satisfying \[ \sup_{t\in T}\int| X(t,\omega)| dP(\omega)<+\infty. \] The space \(B_ 0(T)\) is endowed with the pointwise convergence in the first mean. Suitable conditions of Korovkin type are stated in order that an arbitrary sequence \((L_ n)_{n\in N}\) of positive linear operators from \(B_ 0(T)\) to \(B_ 0(T)\) converge to the identity operator, i.e., \(L_ n(X)\to X\) in \(B_ 0(T)\), for every \(X\in B_ 0(T)\).
Mathematics Subject Classification ID: 60F25
Mathematics Subject Classification ID: 41A36
Mathematics Subject Classification ID: 60G99
zbMATH DE Number: 38589
zbMATH Keywords: stochastic Korovkin theorem
zbMATH Keywords: pointwise convergence in the first mean
zbMATH Keywords: positive linear operators
MaRDI profile type: Publication
OpenAlex ID: W1979702365
description: scientific article; zbMATH DE number 38589