TY  - JOUR
AV  - none
TI  - Asymptotics for randomly reinforced urns with random barriers
KW  - Bayesian nonparametrics ? Central limit theorem ? Clinical
trial ? Random probability measure ? Stable convergence ? Urn model
.
UR  - http://dx.doi.org/10.1017/jpr.2016.75
SN  - 0021-9002
N2  - 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)?
ID  - eprints3113
EP  - 1220
Y1  - 2016/12//
JF  - Journal of applied probability
IS  - 4
A1  - Berti, Patrizia
A1  - Crimaldi, Irene
A1  - Pratelli, Luca
A1  - Rigo, Pietro
PB  - Applied Probability Trust
SP  - 1206
VL  - 53
ER  -