*Tid:***18 februari 2002 kl 1615-1700 **

*Plats :***Seminarierummet 3733**, Institutionen för
matematik, KTH, Lindstedts väg 25, plan 7. Karta!

*Föredragshållare:***
Henrik Hult.
**

**Titel:** **
Excursions in the Brownian motion and the Brownian bridge and
relations to the two parameter Poisson-Dirichlet distribution.
**

**Sammanfattning:**

The two-parameter Poisson-Dirichlet distribution has been
investigated by J. Pitman, M. Yor and others. It is a distribution of
a random vector (V_{1},V_{2},...) such that V_{1}>V_{2}>... and V_{1}+V_{2}+... = 1.
That is, a distribution of an ordered partition of the interval
[0,1].

It turns out that PD(1/2,0) gives the distribution of a partition of [0,1] given by the excursions of a Brownian motion and PD(1/2,1/2) gives the disirtibution of a partition given by the excursions of a Brownian bridge. We will discuss these results and show how they can be derived as limits of a simple random walk.