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
- Hales T., Kusner W.: Packings of Regular Pentagons in the Plane. In: Contemporary Mathematics, to appear. arXiv:1602.07220.
- Hellekalek P.: On the $3x+1$ problem. Submitted, 2016. arXiv:1605.02634.
- Pethő A., Thuswaldner J., Weitzer M.: Shift radix systems with general parameters. Submitted, 2017. arXiv:1711.09596.
- Keryan K., Passenbrunner M.: Projection operators onto spaces of Chebyshev splines, Submitted, 2018. arXiv:1807.07161.
- 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.
- Dong G. Y., Lemieux C., Wiart J.: On the dependence structure of scrambled (t, m, s)-nets. Submitted, 2019. arXiv:1903.09877.
- 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.
- Grabner P. J.: Purity results for some arithmetically defined measures, Submitted, 2019. arXiv:1908.09023.
- Johnston S., Prochno J.: A Maxwell principle for generalized Orlicz balls, Submitted, 2020. arXiv:2012.11568.
- 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.
- Serdyuk A.S., Stepanyuk T.: Uniform approximations by Fourier sums on classes of convolutions of periodic functions, Submitted, 2020. arXiv:2001.00374v1
- Amri M., Spiegelhofer L., Thuswaldner J.: Sur la répartition jointe de la représentation d'Ostrowski dans les classes de résidu, Submitted. arXiv:2006.06960.
- Spiegelhofer L., Wallner M.: The digits of n+t, In: Ann. Sc. Norm. Super. PIsa CL Sci, to appear. arXiv:2005.07167.
- Aistleitner C., Technau N., Zafeiropoulos A.: On the order of magnitude of Sudler products. In: Amer. J. Math., to appear. arXiv:2002.06602.
- 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.
- Aistleitner C., Baker S., Technau N., Yesha N.: Gap statistics and higher correlations for geometric progressions modulo one, Submitted. arXiv:2010.10355.
- Aistleitner C., Gantert N., Kabluchko Z., Prochno J., Ramanan K.: Large Deviation Principles for Lacunary Sums, Submitted. arXiv:2012.05281.
- Wilfried Imrich, Thomas Lachmann, Thomas W. Tucker, Gundelinde M. Wiegel, Asymmetrizing cost and density of vertex-transitive cubicgraphs, Submitted. PDF.
- 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.
- Krieg D., Sonnleitner M.: Random points are optimal for the approximation of Sobolev functions. In: IMA Journal of Numerical Analysis, ,2023. arXiv:2009.11275.
- Kiuchi I., Saad Eddin S.: On sums of arithmetic functions involving the greatest common divisor, Submitted, 2021. arXiv:2102.03714.
- Desmettre S., Steffensen M.: Optimal Investment with Uncertain Risk Aversion, Submitted, 2021. Link.
- Pollington A., Velani S., Zafeiropoulos A., Zorin A.: Inhomogeneous Diophantine Approximation on M0-sets with restricted denominators, Submitted, 2019. arXiv:1906.01151.
- Neumüller M.: On the asymptotic behaviour of the sine product $\prod_{r=1}^n |2 \sin(\pi r \alpha )|$, Submitted, 2021. arXiv:2103.14307.
- 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.
- Heiny J., Johnston S., Prochno J.: Thin-shell theory for rotationally invariant random simplices, Submitted, 2021. arXiv:2103.11872.
- Breneis S., Prochno J., Rudolf D.: The minimal spherical dispersion, Submitted, 2021. arXiv:2103.11701.
- Johnston S., Kabluchko Z., Prochno J.: Projections of the uniform distribution on the cube - a large deviation perspective, Submitted, 2021. arXiv:2103.16430.
- Prochno J., Strzelecki M.: Approximation, Gelfand, and Kolmogorov numbers of Schatten class embeddings, Submitted, 2021. arXiv:2103.13050.
- Lemieux Ch. and Wiart J.: On the distribution of scrambled (0,m,s)-nets over unanchored boxes. Submitted, 2021.
- Desmettre S., Laudagé C., Sass J.: Scalarized Utility-Based Multi-Asset Risk Measures. Submitted, 2021. Link.
- Aichinger F., Desmettre S.: Utility Maximization in Multivariate Volterra Models. In: SIAM Journal on Financial Mathematics, 14(1), 52-98. 2023. Link.
Lachmann T., Wiart J.: On the area of empty axis-parallel rectangles amidst 2-dimensional lattice points:, Submited, arXiv:2109.11222.
- 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.
- Krieg D., Sonnleitner M.: Function recovery on manifolds using scattered data. Submitted, 2021. arXiv:2109.04106.
- 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.
- Hofer R., Larcher G.: Discrepancy bounds for normal numbers generated by necklaces in arbitrary base. Submitted 2022. Link.
- 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.
- 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.
- 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.
- 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.
- L. Merai, I.E. Shparlinski, A. Winterhof. Character sums over sparse elements of finite fields. Submitted, 2022. arXiv:2211.08452.
- Pillichshammer F.: The BMO-discrepancy suffers from the curse of dimensionality. Submitted, 2022.
- Leobacher G., Pillichshammer F., and Ebert A.: Tractability of $L_2$-approximation and integration in weighted Hermite spaces of finite smoothness. Submitted, 2022.
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.
Aichholzer O., Eppstein D., Hainzl E.-M: Geometric Dominating Sets, In: Computational Geometry, Vol 108, to appear. https://arxiv.org/pdf/2203.13170.pdf.
Buczolich, Z., Leobacher, G., Steinicke, A.: Continuous functions with impermeable graphs. In: Mathematische Nachrichten, 2023, arXiv:2201.02159.
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. https://www.dmg.tuwien.ac.at/drmota/
Drmota M., Lemanczyk M., Müllner C., Rivat J.: Some recent developments on the Sarnak conjecture, submitted 2022. https://www.dmg.tuwien.ac.at/drmota/
Deshouillers J.-M., Drmota M., Müllner C., Shubin A., Spiegelhofer L.: Synchronizing automatic sequences along Piatetski-Shapiro sequences, submitted 2022. https://arxiv.org/abs/2211.01422.
Drmota M., Hainzl E.-M.: Universal asymptotic properties of positive catalytic variable equations, submitted 2022.
https://arxiv.org/abs/2212.07741Holighaus 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.
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.
Aistleitner C., Borda B., Hauke M.: On the distribution of partial quotients of reduced fractions with fixed denominator. arXiv:2210.14095.
Pillichshammer F.: Optimal periodic $L_2$-discrepancy and diaphony bounds for higher order digital sequences. Submitted, 2022.
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.
Anderson A., Dostert, M., Grabner P. J., Matzke R. W., Stepaniuk T. A.: Riesz and Green energy on projective spaces. Submitted, 2022. https://arxiv.org/abs/2204.04015.
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:
- 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
- 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
- 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
- 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.
- Larcher G.: Die Black-Scholes-Theorie: In 100 Schritten vom Münzwurf zum Wirtschaftsnobelpreis. Springer-Gabler-Verlag, 2022.
- Dick J., Kritzer P., Pillichshammer F.: Lattice Rules. Numerical Integration, Approximation, and Discrepancy. Springer, Cham, 2022. ISBN 978-3-031-09950-2.
- Hickernell, F.J, Kritzer, P. (eds.): Multivariate Algorithms and Information-Based Complexity. DeGruyter, Berlin/Boston, 2020. Link
- Dick J., Bilyk D., and Pillichshammer F. (eds.): Discrepancy Theory, De Gruyter, Berlin, 2020. ISBN: 978-3-11-065115-7
- 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:
- Saad Eddin S.: Two problems with Laurent-Stieltjes coefficients. LAP Lambert Academic Publishing.2017.
- 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.
- 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.
- Leobacher G., Pillichshammer F.: Introduction to Quasi-Monte Carlo Integration and Applications. Birkhäuser. 2014.
- 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.
- Schmidt K.-U., Winterhof A. (eds.): Sequences and Their Applications-SETA 2014. Lecture Notes Computer Science: Springer. 2014.
- Niederreiter H., Winterhof A.: Applied Number Theory, Berlin: Springer. 2015.
- 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.