Astrid Hilbert

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

Mathematics at Linnaeus University

Mathematics There is a long tradition of mathematics at Linnaeus University. You can study for a Degree of Bachelor, Master or Master of Science in Engineering, and we also do research in mathematics…

Material from LSAA, Linnaeus University Workshop in Stochastic Analysis and Applications

Organization of conferences outside Linnaeus University

My research groups

My ongoing research projects

Project: Quantum Information Access and Retrieval Theory (QUARTZ) Quantum Information Access and Retrieval Theory (QUARTZ) is a project that aims to educate early stage researchers to adopt a novel,…

Publications

Article in journal (Refereed)

Berrhazi, B., El Fatini, M., Hilbert, A., Mrhardy, N., Pettersson, R. (2023). RBDSDEs with jumps and optional Barrier and mean field game with common noise. Stochastics : An International Journal of Probablitiy and Stochastic Processes. 95 (4). 615-634.
Status: Published
Bouhadou, S., Hilbert, A., Ouknine, Y. (2023). Optimal stopping in predictable setting. Probability, Uncertainty and Quantitative Risk (PUQR). 8 (4). 485-498.
Status: Published
El Attouga, S., Bouggar, D., El Fatini, M., Hilbert, A., Pettersson, R. (2023). Lévy noise with infinite activity and the impact on the dynamic of an SIRS epidemic model. Physica A : Statistical Mechanics and its Applications. 618.
Status: Published
Makhlouf, K., Agram, N., Hilbert, A., Øksendal, B. (2023). SPDEs with space interactions and application to population modelling. ESAIM : Control, Optimisation and Calculus of Variations . 29.
Status: Published
Bouhadou, S., Hilbert, A., Ouknine, Y. (2022). RBSDEs with optional barriers : monotone approximation. Probability, Uncertainty and Quantitative Risk (PUQR). 7 (2). 67-84.
Status: Published
Erraoui, M., Hilbert, A., Louriki, M. (2021). On a Levy process pinned at random time. Forum mathematicum. 33 (2). 397-417.
Status: Published
Douissi, S., Agram, N., Hilbert, A. (2020). Mean-field optimal control problem of SDDES driven by fractional brownian motion. Probability and Mathematical Statistics. 40 (1). 139-158.
Status: Published
Berrhazi, B., El Fatini, M., Hilbert, A., Mrhardy, N., Pettersson, R. (2020). Reflected backward doubly stochastic differential equations with discontinuous barrier. Stochastics : An International Journal of Probablitiy and Stochastic Processes. 92 (7). 1100-1124.
Status: Published
Agram, N., Hilbert, A., Øksendal, B. (2020). Singular control of SPDEs with space-mean dynamics. Mathematical Control & Related Fields. 10 (2). 425-441.
Status: Published
Erraoui, M., Hilbert, A., Louriki, M. (2020). Bridges with Random Length : Gamma Case. Journal of theoretical probability. 33. 931-953.
Status: Published
Hilbert, A., Jarni, I., Ouknine, Y. (2020). On reflected stochastic differential equations driven by regulated semimartingales. Statistics and Probability Letters. 167. 1-7.
Status: Published
Es-Sebaiy, K., Farah, F., Hilbert, A. (2020). Weyl Multifractional Ornstein-Uhlenbeck Processes Mixed with a Gamma Distribution. Probability and Mathematical Statistics. 40 (2). 269-295.
Status: Published
Assing, S., Hilbert, A. (2018). On the collapse of trial solutions for a damped-driven nonlinear Schrödinger equation. Nonlinearity. 31 (11). 4955-4978.
Status: Published
Doerr, B., Fischer, P., Hilbert, A., Witt, C. (2017). Detecting Structural Breaks in Time Series via Genetic Algorithms. Soft Computing - A Fusion of Foundations, Methodologies and Applications. 21 (16). 4707-4720.
Status: Published
Basna, R., Hilbert, A., Kolokoltsov, V. (2017). An Approximate Nash Equilibrium for Pure Jump Markov Games of Mean-field-type on Continuous State Space. Stochastics : An International Journal of Probablitiy and Stochastic Processes. 89 (6-7). 967-993.
Status: Published
Djechiche, B., Hilbert, A., Nassar, H. (2016). On the Functional Hodrick-Prescott Filter with Non-compact Operators. Random Operators and Stochastic Equations. 24 (1). 33-42.
Status: Published
Basna, R., Hilbert, A., Kolokoltsov, V. (2014). An Epsilon Nash Equilibrium For Non-Linear Markov Games of Mean-Field-Type on Finite Spaces. Communications on Stochastic Analysis. 8 (4). 449-468.
Status: Published
Albeverio, S., Hilbert, A., Kolokoltsov, V. (2012). Uniform Asymptotic Bounds for the Heat Kernel and the Trace of a Stochastic Geodesic Flow. Stochastics : An International Journal of Probablitiy and Stochastic Processes. 84 (2-3). 315-333.
Status: Published
Albeverio, S., Hilbert, A., Kolokoltsov, V. (1999). Estimates uniform in time for the transition probability ofdiusions with small drift and for stochastically perturbed Newton equations. Journal of theoretical probability. 12 (2). 293-300.
Status: Published
Albeverio, S., Hilbert, A., Kolokoltsov, V. (1997). Transcience of stochastically perturbed classical Hamiltonian systems and random wave operators. Stochastics and Stochastics Reports. (1-2). 41-55.
Status: Published

Conference paper (Refereed)

Fischer, P., Hilbert, A. (2014). Fast Detection of Structural Breaks. Proceedings of COMPSTAT 2014, 21th International Conference on Computational Statistics, Geneva, August 19-22, 2014. 9-16.
Doerr, B., Fischer, P., Hilbert, A., Witt, C. (2013). Evolutionary Algorithms for the Detection of Structural Breaks in Time Series : extended abstract. Proceedings of the 15th annual conference on Genetic and evolutionary computation. 119-120.
Fischer, P., Hilbert, A. (2012). Visual time series analysis. Proceedings of COMPSTAT 2012 : 20th International Conference on Computational Statistics. 225-234.
Avis, D., Fischer, P., Hilbert, A., Khrennikov, A. (2009). Single, Complete, Probability Spaces Consistent With EPR-Bohm-Bell Experimental Data. Foundations of Probability and Physics-5. 294-301.
Hilbert, A. (2004). Some features of regular Hamiltonian dynamics corresponding to degenerate diffusions on a cotangent bundle.
Hilbert, A., Léandre, R. (2001). Nagel-Stein-Wainger estimates for balls associated with the Bismut condition. Stochastic Processes, Physics and Geometry: New Interplays II. 269-284.

Conference proceedings (editor) (Refereed)

Hilbert, A., Mastrogiacomo, E., Mazzucchi, S., Rüdiger, B., Ugolini, S. (2023). Quantum and Stochastic Mathematical Physics : Sergio Albeverio, Adventures of a Mathematician, Verona, Italy, March 25–29, 2019. Springer. 385.

Article in journal (Other academic)

Hilbert, A. (2000). Sur le comportement asymptotique du noyau associé à une diffusion dégénérée. Reviews Canadian Math. (4). 151-159.
Status: Published

Conference paper (Other academic)

Al-Talibi, H., Hilbert, A., Kolokoltsov, V. (2010). Nelson-type Limit for a Particular Class of Lévy Processes. AIP Conference Proceedings; 1232. 189-193.

Manuscript (preprint) (Other academic)

Albeverio, S., Hilbert, A., Kolokoltsov, V. (2009). Asymptotic Expansions for the Heat Kernel and the Trace of a Stochastic Geodesic Flow.
Assing, S., Hilbert, A. A time change method for second order SDEs.
Assing, S., Hilbert, A. On the collapse of a wave functionsatisfying a damped driven non-linearSchr ̈odinger equation.
Al-Talibi, H., Hilbert, A. Differentiable Approximation by Solutions of Newton Equations Driven by Fractional Brownian Motion..
Al-Talibi, H., Hilbert, A., Kolokoltsov, V. Smoluchowski-Kramers Limit for a System Subject to a Mean-Field Drift.