Functional Central Limit Theorems for Stick-Breaking Priors

We obtain the strong law of large numbers, Glivenko-Cantelli theorem, central limit functional theorem for various Bayesian nonparametric priors which include stick-breaking process with general weights, two-parameter Poisson-Dirichlet process, normalized inverse Gaussian generalized gamma and Dirichlet process. For we introduce two conditions such that hold. Except in case since finite dimensional distributions these processes are either hard to or complicated use even they available, method moments convergence results. its marginal asymptotics although computations highly technical.