Home | deutsch  |  Impressum  |  Data Protection  |  Sitemap  |  Intranet  |  KIT
Institute of Stochastics

Secretariat
Kollegiengebäude Mathematik (20.30)
Room 2.056 und 2.002

Address
Hausadresse:
Karlsruher Institut für Technologie (KIT)
Institut für Stochastik
Englerstr. 2
D-76131 Karlsruhe

Postadresse:
Karlsruher Institut für Technologie (KIT)
Institut für Stochastik
Postfach 6980
D-76049 Karlsruhe

Office hours:
Mo-Fr 10:00 - 12:00

Tel.: +49 721 608 43270/43265

Fax.: +49 721 608 46066

Workgroup Point Processes and Random Measures

Summary

Point processes and random measures are ubiquitous in all areas of modern probability and its applications. Examples are arrival and departure processes in stochastic (fluid) networks, geometric point processes of particles and flats, as well as local time of Brownian measures and its inverse. One focus of our research is on the interplay between balancing invariant transports of random measures and Palm measures. The underlying theory of stationarity is quite general and applies to random measures on a state space that is subject to a group operation. Specific topics of research are the mass transport principle, mass-stationarity of random measures and invariance properties of Brownian motion and other random processes and fields.

Another focus of our research is the Fock space representation of functionals of general Poisson processes based on iterated difference operators. This representation has some interesting consequences for chaos expansion and martingale theory of Poisson functionals. Currently we are using the Fock space representation as convenient aproach to perturbation theory for Poisson processes and its applications to Levy processes and continuum percolation.