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Astrid Hilbert

Professor
Department of Mathematics Faculty of Technology
+46470708112
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Teaching

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.

Research

My field of research is Stochastic Analysis, that is based on a differential calculus for stochastic processes. We combine methods and generalize results from 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 and technology as well as in economy, for example:

  • hydrological problems in nuclear waste management
  • image analysis and reconstruction, e.g. for tomographs
  • optimal management of electricity networks
  • time evolution in biology, e.g. the spreading of infections
  • prediction of prices, e.g. electricity prices
  • inter-bank monetary transfer
  • appropriate reinsurance levels
  • solvency of insurance business
  • optimal evacuation of large buildings

Commissions

  • Gender representative and member of the steering board at Ruhr University, Bochum
  • Member of the steering board of the university library, Växjö University
  • Ccoordinator of the international relations of the department of mathematics, Linnaeus University
  • Member of the employment committee of the faculty of technology, Linnaeus University
  • Member of the network for internationalization, Linnaeus University

Projects and Experiences

  • Project leader of the bilateral project SI-DAAD
  • Several Erasmus projects within Europe
  • Linneaus Palme projects with universities in Ukraine, Russia, Morocco, Tajikistan, and Tunisia
  • Erasmus+ projects with the universities Tunis El Manar, Tunisia, and Cadi Ayyad, Morrocco
  • Member and employee of project of Asyl-, migrations- och integrationsfonden/Asylum, Migration and Integration Fund (AMIF) at Migrationsverket

Publications

Article in journal (Refereed)

Conference paper (Refereed)

Article in journal (Other academic)

Conference paper (Other academic)