Stochastic Data Analysis
Many disordered systems are governed by stochastic as well as deterministic influences. Together with the group of Prof. Friedrich (Institute of Theoretical Physics, University of Münster) we have developed a method which characterizes such systems in a compact and comprehensive way. This method was inspired by Kolmogorov's works on the theory of Markov processes. The systems under investigation are modeled by stochastic differential equations whose parameters are estimated from measured data. Neccessary conditions can also be verified from measurement data without the need of assumptions.
Up to now, manifold systems have been successfully investigated following this method, including turbulence, financial markets, surface roughness, human movements, and many other. The description by stochastic differential equations is compact and especially separates deterministic and stochastic behavior. This point of view enables new insights in the behavior of complex systems.