Currently our research is focused on

• numerics for stochastic partial differential equations

• quadrature problems for stochastic differential equations

• infinite-dimensional integration.

In addition to the construction and analysis of new algorithms, the study of the intrinsic difficulty of the computational problem within the framework of information-based complexity plays an important role in some of our research projects. Applications in engineering and in finance are addressed in joint projects at the Fraunhofer ITWM and within the Center for Mathematical and Computational Modelling.

• Extraction of Quantifiable Information from Complex Systems (more), DFG Priority Program 1324, steering committee

• Constructive Quantization and Multilevel Algorithms for Quadrature of Stochastic Differential Equations, within DFG Priority Program 1324

• Adaptive Wavelet Methods for Stochastic Partial Differential Equations, within DFG Priority Program 1324

• Hardware Assisted Acceleration for Monte Carlo Simulations in Financial Mathematics with a Particular Emphasis on Option Pricing (HOPP), within Center for Mathematical and Computational Modelling (CM^{^2})

• Stochastic Modelling and Approximation of Turbulent Spinning Processes, within Fraunhofer Innovation Center Applied System Modelling

• Monte Carlo Simulation of Asymmetric Flow Field Flow Fractionation, jointly with Fraunhofer ITWM, Department of Flow and Material Simulation

We have been involved in a number of projects on problems in applied stochastics with well-known industrial partners.

The list of projects includes:

• Sales Forecasting for Food Retailers, in cooperaton with REWE-digital and Mathematical Stochastics (Universität Passau)
• Optimal Loading Strategies for Large Systems of Cash Points, in cooperation with Wincor-Nixdorf and Discrete Optimization (TU Darmstadt)
• Estimation of Vehicle-Pedestrian Collision Risk, in cooperation with Continental Safety Engineering
• Weather Data in Sales Forecasting, in cooperation with REWE-digital and Mathematical Stochastics (Universität Passau)
• Modelling and Prediction for Cash Recyclers, in cooperation with Wincor-Nixdorf
• Modelling and Analysis of Pharmacological Production Processes,  in cooperation with Merck, Fraunhofer ITWM and Mathematical Stochastics (Universität Passau)
• Deterministic and Stochastic SIR-Modelling, in cooperation with Boehringer Ingelheim