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Mathematical Statistics and Probability Theory

Main research areas

The group's research is concerned with both modern topics in mathematical statistics, as well as with fundamental aspects of probability theory.

Concerning mathematical statistics, the main research areas comprise the development of new statistical methods, proving their validity and their application to real life data situations, for instance from finance, hydrology or meteorology. Typically, the developed methods aim at assessing the behavior of multivariate time series with a possibly nonstationary behavior over time.

More specific research interests are:

  • Extreme-value Statistics
  • Nonparametric Statistics, in particular for copula functions
  • Empirical processes
  • Time Series Analysis
  • Change Point Detection
  • Statistics for Stochastic Processes

Concerning aspects of probability theory, the chair's research aims at a better understanding of stochastic processes. The latter form the backbone of many models for random real-life phenomena, like for instance in finance or physics. Of particular interest are respective (central) limit theorems, which provide general asymptotic laws that are met for a sufficiently large class of models.

Further research fields are:

  • Lévy processes
  • Selfsimilar and semi-selfsimilar processes
  • Stochastic solutions of fractional diffusion equations
  • Fractal path properties of stochastic processes
  • Integral representations of stationary processes

Further details concerning the chair's research can be found on the personal webpages of the staff: Prof. Axel Bücher, Prof. Peter Kern and Prof. i.R. Arnold Janssen.


Third party funding

  • „DigStat - Digitale Lerneinheiten in der Statistik.nrw“
    Subproject for funding line „OERContent.nrw“, 04/2022 - 03/2024, funded by Ministry of Culture and Science NRW together with Digitalen Hochschule NRW.
    For further details, please, click here (Article Mathematicel Institute) and here (press release Ministry of Culture and Science NRW).
    Principal investigators:: Prof. Axel Bücher and JProf. Kathrin Möllenhoff
  • "Statistische Inferenz für Extremwerte von Zeitreihen basierend auf gleitenden Blockmaxima"
    Einzelprojekt (Sachbeihilfe), 10/2021 - 09/2024, funded by Deutschen Forschungsgemeinschaft.
    Principal Investigator: Prof. Axel Bücher
  • "Digitale Materialien in der Stochastik-Lehre für Präsenzveranstaltungen und Selbststudium.nrw"
    Subproject for funding line „OERContent.nrw“, 10/2020 - 09/2022, funded by Ministry of Culture and Science NRW
    For further details, please, click here (MKW Website) or visit the project's website.
    Principal investigators: Prof. Axel Bücher and Prof. Peter Kern
  • "Statistical modeling of spatio-temporal weather extremes - Inference for serial clustering and homogeneity analysis"
    Subproject B3.3 within the BMBF-integrated project "Climate Change and Extreme Events - ClimXtreme Modul B - Statistics“, 03/2020 - 02/2023, funded by Bundesministerium für Bildung und Forschung.
    For further details, please, click here (HHU press release in German) or visit the website ClimXtreme.
    Principal investigator: Prof. Axel Bücher
  • "Statistical modelling of capital market dependence structure via copulas"
    Subproject A7 within the SFB 823 "Statistical modelling of nonlinear dynamic processes" 07/2013 - 06/2021, funded by the German Science Foundation.
    For further details, please, click here.
    Principal instigator: Prof. Axel Bücher
  • "Dimension multivariater selbstähnlicher Prozesse"
    DFG Sachbeihilfe, 2013 - 2016,
    Principal investigator: Prof. Peter Kern
  • "Dilatively stable processes"
    DAAD-MÖB Kooperationsprojekt mit Wissenschaftlern aus Szeged und Debrecen (PPP Ungarn), 2014 - 2015,
    Principal investigator: Prof. Peter Kern


More research activities

Oberseminar "Special Topics in Stochastics"

Jointly with Prof. Holger Schwender (Applied Statistics, Chair of Mathematical Optimization), the chair organizes a weekly research seminar on special topics in stochastics. Talks are given both by master and Phd-students in Düsseldorf, as well as by invited experts from other universities. For further details, please, click here.

StAnDS Workshop „Stochastik und Analysis Düsseldorf-Siegen“

This yearly workshop is organized jointly with the Fachgruppe Stochastik at University of Siegen and takes place either in Düsseldorf or Siegen. The workshop provides a forum for the groups' members to present and discuss their latest research results. For further details, please, click here.

Interdisciplinary statistical colloquium

Please, find here a summary of all previous colloquium lectures that have been compiled for the 50th anniversary in 2018.

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