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Information for Students

Lecture cycle on spatial stochastics #

My three-semester lecture cycle covers mainly the probability theory of random objects in space. A large part of this theory is built on point processes (random point clouds in $\mathbb{R}^d$ or a more general space). In the accompanying seminars we treat complementary topics of stochastic simulation and statistics of objects in Euclidean space.

SpatStoch I #

  • Advanced probability theory
  • Markov chains (discrete time and space), pure-jump Markov processes (continuous time, discrete space)
  • Introduction to point processes in $\mathbb{R}^d$
  • Introduction to random fields (random functions on $\mathbb{R}^d$)

SpatStoch II (mostly accessible without SpatStoch I) #

  • All the important theory of point processes on general state spaces
  • Palm theory and Papangelou kernels
  • Gibbs point processes on $\mathbb{R}^d$
  • Convergence in distribution and limit theorems for point processes

SpatStoch III #

  • Markov chains and pure-jump Markov processes on a continuous space
  • Spatial birth-and-death processes
  • Random closed sets
  • Germ-grain models and Boolean models
  • Random tessellations

Former Bachelor’s and Master’s thesis topics #

Below is the complete(?) list of theses I have supervised. The names of the students have been omitted due to European data protection laws except for published theses.

Master #

  • Pit Neumann, Predicting opioid overdose locations using the INLA-SPDE method for fast Bayesian inference in point process models (2025)
  • Iterative Boltzmann Inversion — A spatial statistics perspective (2023)
  • Theory for Hamiltonian MCMC algorithms for Gibbs processes (2023)
  • The Implementation of a Risk Analysis in the Reinsurance Sector using Copulas (2022); joint supervision with Prof. Michael Fröhlich
  • Structural Inference for Temporal Knowledge Graphs: a Deep Learning Method and a Stochastic Theory Framework (2022)
  • Pricing Approaches for the Insurance Division Aviation in Primary Insurance and Reinsurance (2022); joint supervision with Prof. Michael Fröhlich
  • Spatial Modelling of Gaussian Markov Random Fields using INLA and SPDEs (2021)
  • Uniqueness of Gibbs Measures: Sufficient Conditions (2021)
  • Estimation of Photovoltaic-Generated power: Convolutional Neural Network vs Kriging (2021)
  • Varianzanalyse in euklidischen und nichteuklidischen metrischen Räumen (2021)
  • Wasserstein Learning for Generative Point Process Models (2020)
  • Uniqueness of Gibbs measures via Disagreement Percolation (2020)
  • Binned Estimation of the Pair Correlation Function and Iterative Boltzmann Inversion (2020)
  • A Probabilistic Look at Mutual Information with Application to Point Process (2017)
  • Selective Importance Sampling for Computing the Maximum Likelihood Estimator in Point Process Models (2017)
  • Convergence Rates for Point Processes Thinned by Logit-Gaussian Random Fields (2016)
  • Maximum-Likelihood-Schätzung von exponentiellen Familien von stochastischen Prozessen (2016)
  • Maximum Likelihood Estimation for Spatial Point Processes using Monte Carlo Methods (2016)
  • Statistical Inference of Linear Birth-And-Death Processes (2015)
  • Konvergenzgeschwindigkeit für Markov-Chain Monte Carlo (2015)
  • Tests auf Unabhängigkeit zwischen Punkten und Marken (2015)
  • Thinning of Point Processes by [0,1]-Transformed Gaussian Random Fields (2014)
  • Additivity and Ortho-Additivity in Gaussian Random Fields (2013); joint supervision with Prof. David Ginsbourger
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Bachelor #

  • An Application of Space-Time Point Processes: The ETAS-Model for Earthquake Prediction (2025)
  • Konvergenzraten auf Grundlage der Minorisierungsbedingung für Markovketten auf abzählbarem Zustandsraum (2024)
  • Continuum percolation theory (2024)
  • Predictability of PRNGs using neural networks (2024)
  • Exploring Spatio-Temporal Kriging: Theory and Application to Nitrogen Dioxide Data in the Greater Frankfurt Area (2023)
  • Lennart Finke, Markov Models for Spaced Repetition Learning (2023); joint supervision with Prof. Anja Sturm
  • Noisy Hamiltonian Monte Carlo with an application for point processes (2023)
  • Maximum Likelihood Estimation for Hawkes Processes and Real Data Application (2022)
  • Entrywise Relative Error Bounds for the Stationary Distribution of Perturbed Markov Chains on a Finite State Space. (2022)
  • Second Order Moment Measures of Point Processes (2022)
  • Obere Schranken bei der Bewertung von Stoploss-Verträgen in der Rückversicherung (2022); gemeinsame Betreuung mit Prof. Michael Fröhlich
  • Statistical Analysis of Simulation Algorithms for Finite Random Fields — with a Focus on the Swendsen-Wang Algorithm for the Ising Model (2022)
  • Sequential Monte Carlo Methods and Their Applications in Stock Markets (2022)
  • Comparison of Metropolis Chain and Glauber Dynamics for Proper q-Colorings on a Graph (2021)
  • Das Tobit-Modell: Methodische Anwendungen und Vergleiche zu linearen Regressionen (2021)
  • Markov-Ketten mit allgemeinem Zustandsraum (2021)
  • A comparison between Metropolis–Hastings and Hamiltonian Monte Carlo (2020)
  • Vorhersage im Besag-York-Mollié-Modell (2018)
  • Spline-Regression (2018)
  • Nichtparametrische Regression - Kernregression und lokale Polynome (2018)
  • Theorie und Simulation von Gaußschen Markov-Zufallsfeldern (2018)
  • Comparison of Logistic Regression and Maximum Pseudolikelihood for Spatial Point Processes (2017)
  • Metropolis-Hastings Algorithms for Spatial Point Processes (2016)
  • Valentin Hartmann, A Geometry-Based Approach for Solving the Transportation Problem with Euclidean Cost (2016)
  • A Comprehensive Overview of Linear Birth-and-Death Processes with an Outlook to the Non-Linear Case (2015)
  • Limit Behaviour of Discrete Models in Financial Mathematics (2015)
  • Gaußsche Zufallsfelder: Differenzierbarkeit von Pfaden (2015)
  • Shuffling Measures and the Total Variation Distance to a Perfectly Randomized Deck of Cards (2015)
  • Numerical Computation of L2-Wasserstein Distance Between Images (2014)
  • Erwartete Treffzeiten in Markovketten und deren Anwendung auf Glücksspiele mit Sicherungsoption (2013)