@article{eprints3113,
          author = {Patrizia Berti and Irene Crimaldi and Luca Pratelli and Pietro Rigo},
         journal = {Journal of applied probability},
       publisher = {Applied Probability Trust},
          number = {4},
           pages = {1206--1220},
          volume = {53},
           month = {December},
            year = {2016},
           title = {Asymptotics for randomly reinforced urns with random barriers},
        keywords = {Bayesian nonparametrics ? Central limit theorem ? Clinical
trial ? Random probability measure ? Stable convergence ? Urn model
.},
             url = {http://eprints.imtlucca.it/3113/},
        abstract = {An urn contains black and red balls. Let Zn be the proportion of black balls at time n and 0{$\leq$}L{\ensuremath{<}}U{$\leq$}1 random barriers. At each time n, a ball bn is drawn. If bn is black and Zn-1{\ensuremath{<}}U, then bn is replaced together with a random number Bn of black balls. If bn is red and Zn-1{\ensuremath{>}}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{$\rightarrow$}a.s.Z for some random variable Z, and Dn?{$\sqrt{}$}n(Zn-Z){$\rightarrow$}}
}