Some Diffusion Processes Associated With Two Parameter Poisson-Dirichlet Distribution and Dirichlet Process

Details Some Diffusion Processes Associated With Two Parameter Poisson-Dirichlet Distribution and Dirichlet Process Some Diffusion Processes Associated With Two Parameter Poisson-Dirichlet Distribution and Dirichlet Process

2009-03-03

arxiv.org/abs/0903.0623v2

Mathematics

Probability

24 pages

Scientific paper

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.

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