%0 Journal Article
%9 Working Paper
%@ 0021-9002
%A Berti, Patrizia
%A Crimaldi, Irene
%A Pratelli, Luca
%A Rigo, Pietro
%D 2016
%F eprints:3113
%I Applied Probability Trust
%J Journal of applied probability
%K Bayesian nonparametrics – Central limit theorem – Clinical  trial – Random probability measure – Stable convergence – Urn model  .
%N 4
%P 1206-1220
%T Asymptotics for randomly reinforced urns with random barriers
%U http://eprints.imtlucca.it/3113/
%V 53
%X 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)→