%P 527-546
%T A central limit theorem and its applications to multicolor randomly reinforced urns
%V 48
%I Applied Probability Trust
%K Bayesian statistics; central limit theorem; empirical distribution; Poisson-Dirichlet process; predictive distribution; random probability measure; stable convergence; urn model
%A Patrizia Berti
%A Irene Crimaldi
%A Luca Pratelli
%A Pietro Rigo
%X Let Xn be a sequence of integrable real random variables, adapted to a filtration (Gn). Define Cn = ?{(1 / n)?k=1nXk - E(Xn+1 | Gn)} and Dn = ?n{E(Xn+1 | Gn) - Z}, where Z is the almost-sure limit of E(Xn+1 | Gn) (assumed to exist). Conditions for (Cn, Dn) ? N(0, U) x N(0, V) stably are given, where U and V are certain random variables. In particular, under such conditions, we obtain ?n{(1 / n)?k=1nX_k - Z} = Cn + Dn ? N(0, U + V) stably. This central limit theorem has natural applications to Bayesian statistics and urn problems. The latter are investigated, by paying special attention to multicolor randomly reinforced urns. 
%L eprints975
%D 2011
%J Journal of applied probability 
%N 2
%R 10.1239/jap/1308662642