Linear functionals and Markov chains associated with Dirichlet processes

By investigating a Markov chain whose limiting distribution corresponds to that of the Dirichlet process we are able directly to ascertain conditions for the existence of linear functionals of that process. Together with earlier analyses we are able to characterize those functionals which are a.s. finite in terms of the parameter measure of the process. We also show that the appropriate Markov chain in the space of measures is only weakly convergent and not Harris ergodic.