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Quasi-Monte Carlo Methods: Theory and Applications

FWF Special Research Program (SFB)

Publications from the SFB in the different periods

Publications in the period 01.01.2023 until today


  1. Hales T., Kusner W.: Packings of Regular Pentagons in the Plane. In: Contemporary Mathematics, to appear. arXiv:1602.07220.
  2. Hellekalek P.: On the $3x+1$ problem. Submitted, 2016. arXiv:1605.02634.
  3. Pethő A., Thuswaldner J., Weitzer M.: Shift radix systems with general parameters. Submitted, 2017. arXiv:1711.09596.
  4. Keryan K., Passenbrunner M.: Projection operators onto spaces of Chebyshev splines, Submitted, 2018. arXiv:1807.07161.
  5. Aistleitner C., Blomer V., Radziwill M.: Triple correlation and long gaps in the spectrum of flat tori. In: J. Eur. Math. Soc., to appear, arXiv:1809.07881.
  6. Dong G. Y., Lemieux C., Wiart J.: On the dependence structure of scrambled (t, m, s)-nets. Submitted, 2019. arXiv:1903.09877
  7. Languasco A., Moree P., Saad Eddin S., Sedunova A.: Computation of the Kummer ratio of the class number for prime cyclotomic fields, Submitted, 2019. arXiv:1908.01152.
  8. Grabner P. J.: Purity results for some arithmetically defined measures, Submitted, 2019. arXiv:1908.09023
  9. Johnston S., Prochno J.: A Maxwell principle for generalized Orlicz balls, Submitted, 2020. arXiv:2012.11568
  10. Alonso-Gutiérrez D., Prochno J.: Thin-shell concentration for random vectors in Orlicz balls via moderate deviations and Gibbs measures, Submitted, 2020. arXiv:2011.07523.
  11. Serdyuk A.S., Stepanyuk T.: Uniform approximations by Fourier sums on classes of convolutions of periodic functions, Submitted, 2020. arXiv:2001.00374v1
  12. Amri M., Spiegelhofer L., Thuswaldner J.: Sur la répartition jointe de la représentation d'Ostrowski dans les classes de résidu, Submitted. arXiv:2006.06960.
  13. Spiegelhofer L., Wallner M.: The digits of n+t, In: Ann. Sc. Norm. Super. PIsa CL Sci, to appear. arXiv:2005.07167.
  14. Aistleitner C., Technau N., Zafeiropoulos A.: On the order of magnitude of Sudler products. In: Amer. J. Math., to appear. arXiv:2002.06602
  15. Aistleitner C., El-Baz D., Munsch M.: A pair correlation problem, and counting lattice points with the zeta function. In: Geom. Funct. Anal., to appear. arXiv:2009.08184.
  16. Aistleitner C., Baker S., Technau N., Yesha N.: Gap statistics and higher correlations for geometric progressions modulo one, Submitted. arXiv:2010.10355.
  17. Aistleitner C., Gantert N., Kabluchko Z., Prochno J., Ramanan K.: Large Deviation Principles for Lacunary Sums, Submitted. arXiv:2012.05281.
  18. Wilfried Imrich, Thomas Lachmann, Thomas W. Tucker, Gundelinde M. Wiegel, Asymmetrizing cost and density of vertex-transitive cubicgraphs, Submitted. PDF.
  19. Ivanisvili P., Lindenberger A., Müller P. F.X., Schmuckenschläger M.: Hyper contractivity on the unit circle for ultraspherical measures: linear case, Submitted. arXiv:2004.05567.
  20. Krieg D., Sonnleitner M.: Random points are optimal for the approximation of Sobolev functions. In: IMA Journal of Numerical Analysis, ,2023. arXiv:2009.11275.
  21. Kiuchi I., Saad Eddin S.: On sums of arithmetic functions involving the greatest common divisor, Submitted, 2021. arXiv:2102.03714.
  22. Desmettre S., Steffensen M.: Optimal Investment with Uncertain Risk Aversion, Submitted, 2021. Link.
  23. Pollington A., Velani S., Zafeiropoulos A., Zorin A.: Inhomogeneous Diophantine Approximation on M0-sets with restricted denominators, Submitted, 2019. arXiv:1906.01151.
  24. Neumüller M.: On the asymptotic behaviour of the sine product $\prod_{r=1}^n |2 \sin(\pi r \alpha )|$, Submitted, 2021. arXiv:2103.14307.
  25. Feigenbaum A.S., Grabner P.J., Hardin D.P.: Eigenfunctions of the Fourier Transform with specified zeros. In: Math. Proc. Cambridge Philos. Soc., to appear, 2021. arXiv:1907.08558.
  26. Heiny J., Johnston S., Prochno J.: Thin-shell theory for rotationally invariant random simplices, Submitted, 2021. arXiv:2103.11872.
  27. Breneis S., Prochno J., Rudolf D.: The minimal spherical dispersion, Submitted, 2021. arXiv:2103.11701.
  28. Johnston S., Kabluchko Z., Prochno J.: Projections of the uniform distribution on the cube - a large deviation perspective, Submitted, 2021. arXiv:2103.16430.
  29. Prochno J., Strzelecki M.: Approximation, Gelfand, and Kolmogorov numbers of Schatten class embeddings, Submitted, 2021. arXiv:2103.13050.
  30. Lemieux Ch. and Wiart J.: On the distribution of scrambled (0,m,s)-nets over unanchored boxes. Submitted, 2021.
  31. Desmettre S., Laudagé C., Sass J.: Scalarized Utility-Based Multi-Asset Risk Measures. Submitted, 2021. Link
  32. Aichinger F., Desmettre S.: Utility Maximization in Multivariate Volterra Models. In: SIAM Journal on Financial Mathematics, 14(1), 52-98. 2023. Link.
  33. Lachmann T., Wiart J.: On the area of empty axis-parallel rectangles amidst 2-dimensional lattice points:, Submited, arXiv:2109.11222.

  34. Hinrichs A., Prochno J., Sonnleitner M.: Random section of $\ell$p-ellipsoids, optimal recovery and Gelfand numbers of diagonal operators. Submitted, 2021. arXiv:2109.14504
  35. Krieg D., Sonnleitner M.: Function recovery on manifolds using scattered data. Submitted, 2021. arXiv:2109.04106
  36. Hofer R., Larcher G.: The exact order of discrepancy for Levin's normal number in base 2. In: Journal de Théorie des Nombres des Bordeaux, to appear. Link.
  37. Hofer R., Larcher G.: Discrepancy bounds for normal numbers generated by necklaces in arbitrary base. Submitted 2022. Link
  38. Krieg D., Siedlecki P., Ullrich M., Woźniakowski H.: Exponential tractability of L2-approximation with function values. In: Advances in Computational Mathematics 49, Article No. 18, 2023. arXiv:205.04141
  39. Dolbeault M., Krieg D., Ullrich M.: A sharp upper bound for sampling numbers in L2. In: Applied and Computational Harmonic Analysis, Volume 63, 2023, Pages 113-134. arXiv:220412621
  40. Kritzer, P.: A note on the CBC-DBD construction of lattice rules with general positive weights. In: Journal of Complexity, 76,101721, 2023. arXiv: 2022. 2208.13610.
  41. P. Kritzer, O. Osisiogu. On a reduced component-by-component digit-by-digit construction of lattice point sets. In: Uniform Distribution Theory18 (1), 97-140, 2023. arXiv:2211.12237.
  42. L. Merai, I.E. Shparlinski, A. Winterhof. Character sums over sparse elements of finite fields. Submitted, 2022. arXiv:2211.08452.
  43. Pillichshammer F.: The BMO-discrepancy suffers from the curse of dimensionality. Submitted, 2022.
  44. Leobacher G., Pillichshammer F., and Ebert A.: Tractability of $L_2$-approximation and integration in weighted Hermite spaces of finite smoothness. Submitted, 2022.
  45. Dick, J., Ebert, A., Herrmann, L., Kritzer, P., Longo, M.: The fast reduced QMC matrix-vector product. In: Journal of Computational and Applied Mathematics 440, 115642, 2024. arXiv:2305.11645.

  46. Aichholzer O., Eppstein D., Hainzl E.-M: Geometric Dominating Sets, In: Computational Geometry, Vol 108,  to appear.

  47. Buczolich, Z., Leobacher, G., Steinicke, A.: Continuous functions with impermeable graphs. In: Mathematische Nachrichten, 2023, arXiv:2201.02159.

  48. Deshouillers J.-M., Drmota M., Müllner C.: Coprimality of consecutive elements in a Piatetski-Shapiro sequence. In: Special volume for Eduard Wirsing, Springer, to appear.

  49. Drmota M., Lemanczyk M., Müllner C., Rivat J.: Some recent developments on the Sarnak conjecture, submitted 2022.

  50. Deshouillers J.-M., Drmota M., Müllner C., Shubin  A., Spiegelhofer L.: Synchronizing automatic sequences along Piatetski-Shapiro sequences, submitted 2022.

  51. Drmota M., Hainzl E.-M.: Universal asymptotic properties of positive catalytic variable equations, submitted 2022.

  52. Holighaus N., Koliander G., Hollomey C. and Pillichshammer F.: Grid-Based Decimation for Wavelet Transforms with Stably Invertible Implementation. IEEE Transactions on Audio, Speech and Language Processing , to appear. arXiv:2301.01640

  53. Aistleitner C., Borda B., Hauke M.: On the metric theory of approximations by reduced fractions: a quantitative Koukoulopoulos-Maynard theorem. In: Compos. Math., to appear. Link

  54. Aistleitner C., Borda B., Hauke M.: On the distribution of partial quotients of reduced fractions with fixed denominator. arXiv:2210.14095.

  55. Pillichshammer F.: Optimal periodic $L_2$-discrepancy and diaphony bounds for higher order digital sequences. Submitted, 2022. 

  56. Borda B.: Empirical measures and random walks on compact spaces in the quadratic Wasserstein metric. In: Ann. inst. Henri Poincare Probab. Stat., to appear. Link.

  57. Anderson A., Dostert, M., Grabner P. J., Matzke R. W., Stepaniuk T. A.: Riesz and Green energy on projective spaces. Submitted, 2022.

Publications in the period 01.01.2022-31.12.2022: PDF

Publications in the period 01.01.2021-31.12.2021: PDF

Publications in the period 01.01.2020-31.12.2020: PDF

Publications in the period 01.01.2019-31.12.2019: PDF

Publications in the period 01.01.2018-31.12.2018: PDF

Publications in the period 01.01.2017-31.12.2017: PDF

Publications in the period 01.01.2016-31.12.2016: PDF

Publications in the period 01.01.2015-31.12.2015: PDF

Publications in the period 01.02.2014-31.12.2014: PDF

Books in the period 01.01.2019 until today:

  1. Larcher G.: The Art of Quantitative Finance Vol.2. Risk, Optimal Portfolios, and Case Studies. Springer Texts in Business and Economics, 2023. ISBN: 978-3-031-23866-6
  2. Larcher G.: The Art of Quantitative Finance Vol.2. Volatilities, Stochastic Analysis and Valuation Tools. Springer Texts in Business and Economics, 2023. ISBN: 978-3-031-23869-7
  3. Larcher G.: The Art of Quantitative Finance Vol.1. Trading, Derivatives and Basic Concepts. Springer Texts in Business and Economics, 2023. ISBN: 978-3-031-23872-7
  4. Dick J., Kritzer P., and Pillichshammer F., Lattice Rules -- Numerical Integration, Approximation, and Discrepancy. Springer Series in Computational Mathematics 58, Springer, Cham, 2022. ISBN: 978-3-031-09950-2.
  5. Larcher G.: Die Black-Scholes-Theorie: In 100 Schritten vom Münzwurf zum Wirtschaftsnobelpreis. Springer-Gabler-Verlag, 2022.
  6. Dick J., Kritzer P., Pillichshammer F.: Lattice Rules. Numerical Integration, Approximation, and Discrepancy. Springer, Cham, 2022. ISBN 978-3-031-09950-2.
  7. Hickernell, F.J, Kritzer, P. (eds.): Multivariate Algorithms and Information-Based Complexity. DeGruyter, Berlin/Boston, 2020. Link
  8. Dick J., Bilyk D., and Pillichshammer F. (eds.): Discrepancy Theory, De Gruyter, Berlin, 2020. ISBN: 978-3-11-065115-7
  9. Larcher G.: Quantitative Finance: Strategien, Investments, Analysen. Springer-Gabler-Verlag, 2020. ISBN: 978-3-658-29157-0


Books in the period 01.02.2014-31.01.2018:

  1. Saad Eddin S.: Two problems with Laurent-Stieltjes coefficients. LAP Lambert Academic Publishing.2017.
  2. Kritzer P., Niederreiter H., Pillichshammer F., Winterhof A. (eds.):Uniform Distribution and Quasi-Monte Carlo Methods: Discrepancy, Integration and Applications. Radon Series on Computational and Applied Mathematics (15) Berlin. 2014.
  3. Larcher G., Pillichhammer F., Winterhof A., Xing C. (eds.): Applied Algebra and Number Theory. Essays in honor of Harald Niederreiter on the occasion of his 70th birthday. Cambridge: Cambridge University Press, 2014.
  4. Leobacher G., Pillichshammer F.: Introduction to Quasi-Monte Carlo Integration and Applications. Birkhäuser. 2014.
  5. Niederreiter H., Ostafe A., Panario D., Winterhof A. (eds.) Algebraic Curves and Finite Fields: Cryptography and Other Applications. Radon Series on Computational and Applied Mathematics (16), De Gruyter, Berlin. 2014.
  6. Schmidt K.-U., Winterhof A. (eds.): Sequences and Their Applications-SETA 2014. Lecture Notes Computer Science: Springer. 2014.
  7. Niederreiter H., Winterhof A.: Applied Number Theory, Berlin: Springer. 2015.
  8. Elsholtz C. and Grabner P.J. (eds): Number Theory – Diophantine Problems, Uniform Distribution and Applications. Festschrift on the occasion of Robert Tichy's 60th birthday. Springer, 2017.

PhD Theses in the period 01.02.2018 until today:

  • Stefan Kremsner: Numerical analysis of backward stochastic differential equations. In Progress. (Supervisor: Gunther Leobacher)
  • Mathias Sonnleitner: The power of random information on the sphere. In progress. (Supervisor: Aicke Hinrichs)
  • Onyekachi Osisiogu: Rank-1 Lattices: Theory, Constructions, and Applications. In progress (Supervisor: Peter Kritzer)
  • Alexander Lindenberger: Reproducing Kernels and Applications to Numerical Problems - Beyond Hilbert Spaces. In progress. (Supervisor: Aicke Hinrichs)
  • Damir Ferizović: Uniform Point Distributions and Energy Estimates on Compact Riemannian Manifolds. 2021. (Supervisor: Peter Grabner)
  • 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)
  • 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) PDF
  • Johannes Fürst: An Empirical Investigation on Fast and Stable Methods for the Calibration of Financial Models. In progress. (Supervisor: Gunther Leobacher)

PhD Theses in the period 01.02.2014-31.01.2018:

  • K.C. Chim: Linear forms in logarithms and applications to Diophantine problems. 2018. (Supervisor: Robert Tichy)
  • Ida Aichinger: Distribution Properties of Particle Movements. 2017. (Supervisor: Gerhard Larcher) PDF
  • Ralph Kritzinger: Point sets and sequences with the optimal order of $L_p$ discrepancy. 2017. (Supervisor: Friedrich Pillichshammer) PDF.
  • Florian Puchhammer: Discrepancy estimates for point sets and sequences. 2017. (Supervisor: Gerhard Larcher) PDF.
  • Richard Hofer: New Bounds on Some Measures of Pseudorandomness. 2017. (Supervisor: Arne Winterhof) PDF.
  • Helene Laimer. High-dimensional algorithms - Tractability and componentwise constructions. 2017. (Supervisor: Peter Kritzer) PDF.
  • 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)
  • Michaela Szölgyenyi: Dividend Maximization in Hidden Markov Models and Analysis of Associated Stochastic Differential Equations. 2015. (Supervisor: Gunther Leobacher and Stefan Thonhauser) Link.