Theory of stochastic processes

Stochastic processes are at the center of probability theory, both from a theoretical and an applied viewpoint. Stochastic processes have applications in many disciplines such as physics, computer science, financial mathematics, and chemistry, but also in biology, in particular, neuroscience, or information theory.

In Münster, we analyze a broad variety of stochastic processes.

In Stochastic Geometry we particularly study random polytopes and tessellations. Two of our main objects of interest are random beta polytopes and Voronoi and Laguerre tessellations. In the former, we study relevant functionals of polytopes with nodes sampled from certain distributions. In the latter, we investigate the influence of attractive or repulsive forces on the point process to the geometry of the tessellations.   

A very active area of research are stochastic processes related to random graphs. Our interest ranges from classical Erdős–Rényi graphs to preferential attachment models. We use random graphs as an environment for spin systems in statistical mechanics. A particularly fascinating model for a are stochastic process related to random graphs is percolation. We investigate percolation on groups to examine their properties as well as those of the related operator algebras.

A natural way to describe stochastic processes in continuous time are stochastic (partial) differential equations. For our research on stochastic partial differential equations we refer to the sections on partial differential equations and stochastic analysis.