# 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.