“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.” (Authors’ abstract).
There is a closely related problem considered by M. H. DeGroot and the reviewer [J. Math. Anal. Appl. 7, 489-498 (1963; Zbl 0129.123)] in which the limiting distribution was obtained as a solution of an integral equation. It was solved for the beta distribution in some special cases, but the general equation was left unsolved. Although the authors do not seem aware of that paper, it will be interesting to explore the relations between both these problems and to solve the integral equation more generally.