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Quasi-Monte Carlo Methods: Theory and Applications

FWF Special Research Program (SFB)

Habilitation Theses

  • Joscha Prochno: High-dimensional Probability & Geometric Functional Analysis - Contributions to the normal, moderate, and large deviations approach in geometric functional analysis and the geometry of Schatten classes. In Progress.
  • Roswitha Hofer: Construction of Low-Discrepancy Point Sets and Sequences, and the Distribution of Subsequences. 2016

PhD Theses

  • Paolo Minelli: Über diophantische Approximation, eine Vermutung von Ito über Dedekind-Summen und Poissonsche Paarkorrelation von Folgen. 2022. (Supervisor: Robert Tichy). 
  • Damir Ferizović: Uniform Point Distributions and Energy Estimates on Compact Riemannian Manifolds. 2021. (Supervisor: Peter Grabner)
  • Abraham Gutierrez Sanchez: Probabilistic Aspects in Automata and Digraphs. 2021. (Supervisors: Daniele D'Angeli, Emanuele Rodaro and Christoph Aistleitner)
  • Stefan Kremsner: Numerical analysis of backward stochastic differential equations. In Progress. (Supervisor: Gunther Leobacher).
  • Mahadi Ddamulira: Diophantine Equations and Linearly Recurrent Sequences. 2020. (Supervisor: Robert Tichy) Link.
  • Johann Verwee: Effective Erdös-Wintner Theorem. 2020. (Supervisor: Michael Drmota and Gerald Tenenbaum)
  • Lisa Kaltenböck: On distribution properties of sequences in the unit cube. 2020. (Supervisor: Gerhard Larcher)
  • Mathias Sonnleitner: The power of random information for numerical approximation and integration. 2022. Summa cum laude. (Supervisor: Aicke Hinrichs)
  • Mario Neumüller: Two Contemporary Issues in Number Theory: Sequences with Low Star Discrepancy and the Asymptotic Behaviour of the Sudler Product. 2019. (Supervisor: Friedrich Pillichshammer)
  • Thomas Lachmann: Pair Correlations, Additive Combinatorics, and Metric Diophantine Approximation. 2019 (Supervisor: Christoph Aistleitner)
  • Michael Preischl: Dependence Modeling and Stochastic Optimal Control with Applications in Finance and Insurance. In progress (Supervisor: Robert Tichy)
  • Onyekachi Osisiogu: Quasi-Monte Carlo Methods: Component-by-Component Algorithms. 2022.  (Supervisor: Peter Kritzer) 
  • Alexander Lindenberger: Reproducing Kernels and Applications to Numerical Problems - Beyond Hilbert Spaces. In progress. (Supervisor: Aicke Hinrichs)
  • K.C. Chim: Linear forms in logarithms and applications to Diophantine problems. 2018. (Supervisor: Robert Tichy)
  • Florian Puchhammer: Discrepancy estimates for point sets and sequences. 2017. (Supervisor: Gerhard Larcher)
  • Ida Aichinger: Distribution Properties of Particle Movements. 2017. (Supervisor: Gerhard Larcher)
  • Dominik Kloimstein: Exact Discrepancy for Small Finite Point Sets. In progress. (Supervisor: Gerhard Larcher)
  • Ralph Kritzinger: Point sets and sequences with the optimal order of $L_p$ discrepancy. 2017. (Supervisor: Friedrich Pillichshammer)
  • Richard Hofer: New Bounds on Some Measures of Pseudorandomness. 2017. (Supervisor: Arne Winterhof)
  • Michaela Szölgyenyi: Dividend Maximization in Hidden Markov Models and Analysis of Associated Stochastic Differential Equations. 2015. (Supervisor: Gunther Leobacher and Stefan Thonhauser)
  • Johannes Fürst: An Empirical Investigation on Fast and Stable Methods for the Calibration of Financial Models. In progress. (Supervisor: Gunther Leobacher)
  • Helene Laimer: High-dimensional algorithms - Tractability and componentwise constructions. 2017. (Supervisor: Peter Kritzer)
  • Markus Hittmeir: On the Complexity of Integer Factorization and Related Problems. 2017. (Supervisor: Peter Hellekalek)
  • Alexander Bors: On Dynamical Aspects of Finite Group Endomorphisms. 2016. (Supervisor: Peter Hellekalek)

Diploma Theses

  • Lorenz Frühwirth: An asymptotic thin shell condition and large deviations for random multidimensional projections. 2021 (Joscha Prochno)
  • Simon Breneis: Functions of bounded variation in one and multiple dimensions. 2020 (Supervisor: Aiche Hinrichs, Robert Tichy)
  • Michael L. Juhos: On Fresen’s Proof of the CLT for Convex Bodies. 2020 (Supervisor: Joscha Prochno)
  • Alexander Brunhuemer: Computer-Supported Testing of Option Strategies. 2020. (Supervisor: Gerhard Larcher)
  • Samuel Höller: Assessment and Fair Pricing of Interest Derivates in Continuous Time. 2019. (Supervisor: Gerhard Larcher)
  • Mathias Sonnleitner: Discrepancy and Numerical Integration on Spheres. 2019. (Supervisor: Aicke Hinrichs)
  • Mustafa Krupic: Copula Sampling, Assignment Problems and Applications in Financial Mathematics. 2018. (Supervisor: Christoph Aistleitner)
  • Mathias Aufreiter: Fast-Überall-Konvergenz von Funktionsreihen. 2018. (Supervisor: Markus Passenbrunner)
  • Roman Kurz: $(n\alpha)$-Sequences in QMC-Theory. 2018. (Supervisor: Friedrich Pillichshammer)
  • Andreas Thoma: Tractability Properties of High-Dimensional Integration and Star Discrepancy. 2018. (Supervisor: Friedrich Pillichshammer)
  • Lisa Kaltenböck: Lower bounds for the discrepancy of $(T,s)$-sequences. 2017. (Supervisor: Gerhard Larcher)
  • Wolfgang Stockinger: Lower bounds for the discrepancy of the Halton Sequence. 2017. (Supervisor: Gerhard Larcher)
  • Philipp Lugmayr: Polynomiale Fermat Quotienten. 2014. (Supervisor: Arne Winterhof)
  • Philipp Birklbauer: Waring's problem in finite fields. 2014. (Supervisor: Arne Winterhof)
  • Andrea Duringer: Lattice point sets and their application to numerical integration. 2013. (Supervisor: Peter Kritzer)
  • Markus Hittmeir: Primzahltests und Faktorisierungsverfahren. 2015. (Supervisor: Peter Hellekalek)
  • Michaela Szölgyenyi. Optimal control of an energy storage facility in a hidden Markov model. 2015. (Supervisor: Rene Böheim)

Bachelor Theses

  • Armin Boninsegna: Monte Carlo Algorithmen. Die Methode der direkten Simulation, 2022. (Betreuer: F. Pillichshammer)

  • Julia Reidinger: The Circle Problem, 2022. (Betreuer: F. Pillichshammer)

  • Thomas Pilgerstorfer: Applications of the Monte-Carlo Method in Finance and Risk Management. 2021. (Supervisor: Sascha Desmettre)

  • Nico Stimmeder: Methoden zur Simulation einer Brownschen Bewegung. 2021. (Supervisor: Peter Kritzer, Sascha Desmettre)

  • Simon Breneis: Functions of bounded variation in one and multiple dimensions. 2020. (Supervisor: Aicke Hinrichs)

  • Julian Hofstadler: Bounds for the star-discrepancy in high dimensions. 2019. (Supervisor: Aicke Hinrichs, Mario Ullrich)

  • Lisa Murauer: Nichtlineare Komplexität und Lempel-Ziv Komplexität. 2014. (Supervisor: Arne Winterhof)
  • Victoria Hutterer: Monte Carlo Methoden und Varianzreduktionstechniken. 2014. (Supervisor: Peter Kritzer, Michaela Szölgyenyi)