Project Group B

Project Group B "Stochastic Dynamics, Control and Statistics"

This project group reflects  our vision that the huge potential of ‘rough analysis’ has remained largely unexplored  in important applied fields like statistics, uncertainty quantification, stochastic control theory, financial mathematics and mean field games. The role of signatures in algebraic and Bayesian statistics will be studied, including a long-overdue comparison with existing benchmark models (B01). Widely popular ‘rough volatility’ models are studied from a market microstructure perspective (B02). Their non-Markovianity aspects have parallels in ‘dormancy models’ of mathematical biology, the statistical analysis of which naturally entails robustness questions (B07). Tailor-made for rough paths are also mean field games with common noise, next to pathwise stochastic control (B04, B05). Expected signatures will be used to efficiently solve stochastic control problems (B03). Statistics and UQ aspects of stochastic PDEs will be studied, novel aspects include rough/stochastic boundaries (B06). Model reduction, mean-field dynamics and  their statistical properties (B09), including Bayesian methods with robust parameter identification (B08), conclude our portrait of group B.