Almost sure convergence of urn models in a random environment
type: Item
instance of: scholarly article
title: Almost sure convergence of urn models in a random environment
zbMATH Open document ID: 1008.60017
DOI: 10.1023/A:1016147501945
published in: Journal of Mathematical Sciences (New York)
publication date: 2002-11-25T00:00:00Z
review text: The classical Pólya urn model can be described as follows. An urn contains balls of two colors, black and white. In each step a ball is drawn from the urn. If it is black, we add \(a>0\) black balls to the urn and none white, and if it is white, we add \(a\) of the white ones. This replacement policy can be in general described through the replacement matrix \(R=(r_{ij})\), \(i,j=1,2\), giving the number \(r_{ij}\) of balls of color \(j\) to add if ball of color \(i\) is drawn. The authors present the same setting defined in an analogue fashion for \(L\geq 2\) colors. The Robbins-Monro scheme of stochastic approximation theory is used to obtain an a.s.\ convergence result for the initial model, as well as for the generalization (with the wider class of replacement matrices).
reviewed by: Miloš Stojaković
Mathematics Subject Classification ID: 60C05
Mathematics Subject Classification ID: 60K37
Mathematics Subject Classification ID: 60F15
zbMATH DE Number: 1821724
zbMATH Keywords: urn model
zbMATH Keywords: Robbins-Monro scheme
zbMATH Keywords: convergence
author: José A. Moler
author: Fernando Plo
author: Miguel San Miguel
MaRDI profile type: Publication
full work available at URL: a:1016147501945
OpenAlex ID: W48179499
description: scientific article; zbMATH DE number 1821724