  The two parameter Poisson-Dirichlet distribution $PD(\alpha,\theta)$ is the
distribution of an infinite dimensional random discrete probability. It is a
generalization of Kingman's Poisson-Dirichlet distribution. The two parameter
Dirichlet process $\Pi_{\alpha,\theta,\nu_0}$ is the law of a pure atomic
random measure with masses following the two parameter Poisson-Dirichlet
distribution. In this article we focus on the construction and the properties
of the infinite dimensional symmetric diffusion processes with respective
symmetric measures $PD(\alpha,\theta)$ and $\Pi_{\alpha,\theta,\nu_0}$. The
methods used come from the theory of Dirichlet forms.
