Date: 2012-02-10

Time: 14:00-16:30

Location: Concordia

Abstract:

Stute: The Poisson Process constitutes a well-known model for describing random events over time. It has many applications in marketing research, insurance mathematics and finance. Though it has been studied for decades not much is known how to check (in a non-asymptotic way) the validity of the Poisson Process. In this talk we present the principal component decomposition of the Poisson Process which enables us to derive finite sample properties of associated goodness-of-fit tests. In the first step we show that the Fourier-transforms of the components contain Bessel and Struve functions. Inversion leads to densities which are modified arc sin distributions.

Blath: In this talk we consider properties of the so-called ‘symbiotic branching model’ describing the spatial evolution of two populations which can only reproduce if they are both present at the same location at the same time. We will put particular emphasis on the long-term dynamics of this population model. To this end, we consider a ‘critical curve’ separating the asymptotic behaviour of the moments of the symbiotic branching process into two qualitatively different regimes. From this result, various properties can be derived. For example, we improve a result of Etheridge and Fleischmann on the speed of the propagation of the area in which both species are simultaneously present.

Speaker

Winfried Stute is Professor of Statistics and Probability at the Universität Giessen.

Jochen Blath is Professor of Mathematics at the Technische Universität Berlin.