Many real life phenomena encountered for instance on trading floors, in materials undergoing phase transitions, in the genealogy of populations or in terrestrial glacial records can only be adequately and efficiently 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 different levels:
- Microscopic modeling: interacting systems of individual agents or particles, random walks, random media
- Mesoscopic modeling: (backward) stochastic (partial, delay) differential equations, stochastic flows, rough path equations
The goal of the IRTG is to train PhD students to acquire the mathematical skills needed to
- analyze complex processes in real applications
- develop adequate stochastic models
- treat them with the tools of modern stochastic analysis and stochastic interacting systems
- apply numerical and statistical methods to calibrate models to real data.
Students of the IRTG will be equipped with the mathematical tools and techniques on all levels of stochastic modeling mentioned. A typical PhD thesis will involve problems that are motivated from specific areas of application. These include (but are not limited to)
- financial markets,
- phase transitions and disordered materials,
- climate dynamics and mathematical population biology.
Our research program is structured along two main areas:
- Stochastic analysis and stochastic finance
- Stochastic interacting particle systems in statistical physics and biology
Many cross connections exist between these fields. Although writing a thesis is the main objective of any PhD program, an important component of the IRTG is to expose the students intensively to both areas. In order to achieve this goal we offer a selection of lectures, seminars and special courses from the two fields.