Research program
Many real life phenomena encountered on trading floors, in materials undergoing phase transitions, in the genealogy of populations or in terrestrial glacial records can only be adequately modeled by incorporating elements of randomness. Their stochastic modeling usually starts with the description of system components on different spatial and temporal scales and uses mathematical approaches and techniques on two different levels: microscopic modeling (interacting systems of individual agents or particles, random walks, random media), and meso-/macroscopic modeling ((backward) stochastic (partial, delay) differential equations, stochastic flows, rough paths equations).
PhD students acquire the mathematical skills needed to
- analyze complex processes in applications,
- develop adequate and tractable stochastic models,
- devise tools of stochastic analysis and stochastic interacting systems to treat them,
- and develop statistical methods to calibrate models to real data.
Students of the RTG will be equipped with mathematical tools and techniques on all levels of stochastic modeling. A typical PhD thesis will involve problems motivated from specific areas of application. These include finance (illiquidity, equilibria, stochastic volatility), physics (climate dynamics, crystalline structures, disordered materials), biology (genetics, population biology, neuroscience).
Our research programme will be focused on three main domains:
- stochastic finance,
- stochastic analysis and statistical inference for stochastic dynamics,
- stochastic processes in physics and biology.
Many cross connections exist between these fields. Although writing a thesis is the main objective, an important aspect of this RTG is to expose students intensively to all areas.
