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.
The two-parameter Poisson-Dirichlet distribution has been investigated by J. Pitman, M. Yor and others. It is a distribution of a random vector (V1,V2,...) such that V1>V2>... and V1+V2+... = 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.
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