relation: http://eprints.imtlucca.it/3113/
title: Asymptotics for randomly reinforced urns with random barriers
creator: Berti, Patrizia
creator: Crimaldi, Irene
creator: Pratelli, Luca
creator: Rigo, Pietro
subject: HA Statistics
subject: QA Mathematics
description: An urn contains black and red balls. Let Zn be the proportion of black balls at time n and 0≤L<U≤1 random barriers. At each time n, a ball bn is drawn. If bn is black and Zn-1<U, then bn is replaced together with a random number Bn of black balls. If bn is red and Zn-1>L, then bn is replaced together with a random number Rn of red balls. Otherwise, no additional balls are added, and bn alone is replaced. In this paper we assume that Rn=Bn. Then, under mild conditions, it is shown that Zn→a.s.Z for some random variable Z, and Dn≔√n(Zn-Z)→
publisher: Applied Probability Trust
date: 2016-12
type: Article
type: PeerReviewed
identifier:   Berti, Patrizia and Crimaldi, Irene and Pratelli, Luca and Rigo, Pietro  Asymptotics for randomly reinforced urns with random barriers.  Journal of applied probability, 53 (4).  pp. 1206-1220.  ISSN 0021-9002      (2016)  
relation: http://dx.doi.org/10.1017/jpr.2016.75
relation: 10.1017/jpr.2016.75