This research focus links two of the core areas of mathematics: analysis and stochastics. In research, we study analytic, stochastic and geometrical problems, combining theoretical and application-oriented, algorithmic aspects. Deterministic and stochastic models of continuous mathematics are developed and systematically analysed.
Specific challenges in a rather theoretical focus are found in the areas of infinite-dimensional and white noise analysis, in the complexity of continuous problems and in relaxation models for nonconvex problems. The application-oriented research focuses on data and image analysis by use of harmonic and convex analysis. Likewise, it directs its attention to complex analysis, the construction and analysis of stochastic algorithms, and to the analysis (regularity, long-term behaviour) in the area of (stochastic) partial differential equations.
The analysis and approximation of stochastic and stochastic partial differential equations, which serve as models for random dynamics in finite or infinite-dimensional state spaces, play a particular role. These models find applications in highly diverse areas such as physics, engineering or economic sciences.
Together with the Fraunhofer ITWM, the engineering sciences and our industrial partners, we work on application-oriented topics in joint cooperation. In research and in applications for third-party funding, the aim is to work closely together with the research focuses Industrial Mathematics and Economathematics.