%P 1206-1220
%T Asymptotics for randomly reinforced urns with random barriers
%I Applied Probability Trust
%V 53
%K Bayesian nonparametrics ? Central limit theorem ? Clinical
trial ? Random probability measure ? Stable convergence ? Urn model
.
%A Patrizia Berti
%A Irene Crimaldi
%A Luca Pratelli
%A Pietro Rigo
%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)?
%L eprints3113
%D 2016
%J Journal of applied probability
%R 10.1017/jpr.2016.75
%N 4