The stochastics groups are working on the numerical approximation of stochastic partial differential equations as well as the interplay between geometry and stochastic processes. The central research interests are high-dimensional stochastic and statistical analysis, potential theory and topological aspects of spaces of algebraic and metric measure spaces. The research leads to applications in finance, engineering, biology and physics. There are several areas of overlap between the interests and methods of the different research groups.

Prof. Denis Belomestny is involved in the DFG-funded Collaborative Research Centre CRC 823 with the projects “Statistical modeling of high-resolution spectro-temporal audio data in hearing aids” and “Statistics of complex stochastic models in financial mathematics”.

Several projects have been awarded by the DFG as individual grants. The project “Bayesian inference for generalised tempered stable Levy processes” of Prof. Denis Belomestny starts in January 2019. The goal of the project is development of new, efficient methods of Bayesian inference for Lévy processes based on their discrete-time observations and theoretical investigation of these methods. Prof. Mikhail Urusov is starting the project on “Markov Chain approximation of one-dimensional diffusions with singularities”, which aims at approximating continuous strong Markov processes, especially those exhibiting “singular” behaviour (e.g., “slow reflection” at the boundary of the state space, or “stickiness” inside the state space). In another DFG project, Prof. Martin Hutzenthaler is investigating “On numerical approximations of high-dimensional nonlinear parabolic partial differential equations and of backward stochastic differential equations”. This project sets out to demonstrate how high-dimensional (dimension ≥100) partial differential equations can be numerically approximated without suffering the curse of dimensionality.

Prof. Hutzenthaler and Prof. Anita Winter are principal investigators in the DFG-funded Research Training Group RTG 2131 “High-dimensional phenomena in probability – fluctuations and discontinuity”, which is currently in its first funding period and is already supporting six PhD students and three postdocs in Essen as collegiate or associate members. Prof. Hutzenthaler is also the principal investigator on two further projects, “Evolution of altruistic defense traits in structured population” and “The effect of natural selection on genealogies”, and Prof. Anita Winter on the project “Evolving pathogen phylogenies: a two-level branching approach” within the DFG-funded Priority Programme SPP 1590 “Probabilistic Structures in Evolution”.

Finally, Anton Klimovsky from Prof. Winter’s research group has successfully applied for a grant with the project “Stochastic processes on evolving networks” as part of the DFG’s Scientific Networks programme.