  Matrix Dirichlet processes, in reference to their reversible measure, appear
in a natural way in many different models in probability. Applying the language
of diffusion operators and the method of boundary equations, we describe
Dirichlet processes on the simplex and provide two models of matrix Dirichlet
processes, which can be realized by various projections, through the Brownian
motion on the special unitary group, the polar decomposition of complex
matrices and also through Wishart processes.
