# BNR

## Seminar

### Distributions of linear functionals of the two parameter Poisson-Dirichlet process

Seminar Room 2, Newton Institute Gatehouse

#### Abstract

In this talk, exact expressions for the probability distribution of linear functionals of the two parameter PoissonDirichlet process are illustrated. Indeed, we obtain distributional results yielding exact forms for density functions of these functionals. Moreover, a few interesting integral identities are provided by exploiting a correspondence between the mean of a PoissonDirichlet process and the mean of a suitable Dirichlet process. Finally, some distributional characterizations in terms of mixture representations are proved. The usefulness of these results is highlighted by means of some illustrative examples. Indeed, our formulae are relevant to occupation time phenomena connected with Brownian motion and more general Bessel processes, as well as to models arising in Bayesian nonparametric statistics. The presentation is based on a paper available at: http://www.e-publications.org/ims/submission/index.php/AAP/user/submissionFile/913?confirm=de5c802d