@article{eprints975,
           pages = {527--546},
          number = {2},
          volume = {48},
            year = {2011},
           title = {A central limit theorem and its applications to multicolor randomly reinforced urns},
          author = {Patrizia Berti and Irene Crimaldi and Luca Pratelli and Pietro Rigo},
         journal = {Journal of applied probability },
       publisher = {Applied Probability Trust},
        abstract = {Let Xn be a sequence of integrable real random variables, adapted to a filtration (Gn). Define Cn = {$\sqrt{}$}\{(1 / n)?k=1nXk - E(Xn+1 {\ensuremath{|}} Gn)\} and Dn = {$\sqrt{}$}n\{E(Xn+1 {\ensuremath{|}} Gn) - Z\}, where Z is the almost-sure limit of E(Xn+1 {\ensuremath{|}} Gn) (assumed to exist). Conditions for (Cn, Dn) {$\rightarrow$} 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 {$\sqrt{}$}n\{(1 / n)?k=1nX\_k - Z\} = Cn + Dn {$\rightarrow$} 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. },
             url = {http://eprints.imtlucca.it/975/},
        keywords = {Bayesian statistics; central limit theorem; empirical distribution; Poisson-Dirichlet process; predictive distribution; random probability measure; stable convergence; urn model}
}