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Astrid Hilbert

Department of Mathematics Faculty of Technology
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I have been teaching courses at all levels from the large mathematical fields of analysis, probability theory and statistics, algebra, and discrete mathematics. At the time being, I am almost entirely teaching courses of the Master Programme in Mathematics and Modelling, specialisation in Mathematical Statistics and Financial Mathematics, a specialisation for which I am responsible.


I have been working at the borderline between probability theory and functional analysis, in particular operator theory. These fields also constitute the basic mathematical toolboxes for quantum mechanical models. More precisely, my area of research is stochastic dynamic systems driven by stochastic processes, e.g. degenerate Brownian motion as starting point and more general Lévy and non-Markovian noises like fractional Brownian motion and non-linear processes involving a mean-field contribution. The existence of solutions is studied while the focus is on qualitative properties of the system like transience, ergodicity, asymptotic dependence on parameters like time, scaling parameters, number of particles/players.

Due to their importance in applications, optimization problems were investigated recently, i.e. optimal filtering and stochastic optimal control as part of differential games. Motivated by applications and applicability, my field of research was completed by time series models, better accessible for statistical inference. My focuses are functional data analysis and computational statistics for high frequency and large data sets.

There are numerous applications in the natural sciences as well as in economy, e.g. to hydrological problems in nuclear waste management, or the prediction of prices, e.g. electricity prices, inter-bank monetary transfer, appropriate reinsurance levels, solvency of insurance business, and optimal evacuation of large buildings.


Article in journal (Refereed)

Conference paper (Refereed)

Article in journal (Other academic)

Conference paper (Other academic)