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)
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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)→
| Item Type: | Article |
|---|---|
| Identification Number: | https://doi.org/10.1017/jpr.2016.75 |
| Projects: | crisis lab |
| Uncontrolled Keywords: | Bayesian nonparametrics – Central limit theorem – Clinical trial – Random probability measure – Stable convergence – Urn model . |
| Subjects: | H Social Sciences > HA Statistics Q Science > QA Mathematics |
| Research Area: | Economics and Institutional Change |
| Depositing User: | Irene Crimaldi |
| Date Deposited: | 24 Feb 2016 12:03 |
| Last Modified: | 19 Dec 2016 10:00 |
| URI: | http://eprints.imtlucca.it/id/eprint/3113 |
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Asymptotics for randomly reinforced urns with random barriers. (deposited 03 Sep 2015 09:50)
- Asymptotics for randomly reinforced urns with random barriers. (deposited 24 Feb 2016 12:03) [Currently Displayed]
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