Process of random distributions : classification and prediction

We define a continuous time stochastic process such that each is a Ferguson-Dirichlet random distribution. The parameter of this process can be the distribution of any usual such as the (multifractional) Brownian motion. We also extend Kraft random distribution to the continuous time case. We give an application in classifiying moving distributions by proving that the above random distributions are generally mutually orthogonal. The proofs hinge on a theorem of Kakutani.