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.
Groupe d’études et de recherche en analyse des décisions