eprintid: 3113
rev_number: 6
eprint_status: archive
userid: 36
dir: disk0/00/00/31/13
datestamp: 2016-02-24 12:03:56
lastmod: 2016-12-19 10:00:37
status_changed: 2016-02-24 12:03:56
type: article
succeeds: 2742
metadata_visibility: show
creators_name: Berti, Patrizia
creators_name: Crimaldi, Irene
creators_name: Pratelli, Luca
creators_name: Rigo, Pietro
creators_id: 
creators_id: irene.crimaldi@imtlucca.it
creators_id: 
creators_id: 
title: Asymptotics for randomly reinforced urns with random barriers
ispublished: pub
subjects: HA
subjects: QA
divisions: EIC
full_text_status: none
monograph_type: working_paper
keywords: Bayesian nonparametrics – Central limit theorem – Clinical
trial – Random probability measure – Stable convergence – Urn model
.
abstract: 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)→
date: 2016-12
date_type: published
publication: Journal of applied probability
volume: 53
number: 4
publisher: Applied Probability Trust
pagerange: 1206-1220
pages: 13
id_number: 10.1017/jpr.2016.75
institution: IMT Institute for Advanced Studies Lucca
refereed: TRUE
issn: 0021-9002
official_url: http://dx.doi.org/10.1017/jpr.2016.75
related_url_url: http://projecteuclid.org/euclid.jap/1481132847
projects: crisis lab
citation:   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)