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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 01.01.2021 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. Matsumoto K., Saad Eddin S.:  An asymptotic formula for the 2k-th power mean value of $|L^\prime/L(1+it_0, \chi)|$. In: Journal of the Mathematical Society of Japan, 73(3), pp. 781-814, 2021. arXiv:1803.00495.
  5. Kiuchi I., Pillichshammer F., Saad Eddin S.: On the multivariable generalization of Anderson-Apostol sums. In: Far East Journal of Mathematical Sciences, 130(1), pp. 1-24, 2021. arXiv:1811.06022.
  6. Keryan K., Passenbrunner M.: Projection operators onto spaces of Chebyshev splines, Submitted, 2018. arXiv:1807.07161.
  7. Leobacher G., Steinicke A.: Existence, Uniqueness and Regularity of the Projection onto Differentiable Manifolds, Ann. Glob. Anal. Geom. (2021), to appear, arXiv:1811.10578.
  8. Anbar Meidl N., Stichtenoth H., Tutdere S.: Asymptotically good towers of function fields with small $p$-rank, Submitted, 2019. PDF.
  9. Aistleitner C., Blomer V., Radziwill M.: Triple correlation and long gaps in the spectrum of flat tori, submitted, 2018, arXiv:1809.07881.
  10. Dong G. Y., Lemieux C., Wiart J.: On the dependence structure of scrambled (t, m, s)-nets. Submitted, 2019. arXiv:1903.09877
  11. 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.
  12. Inoue S., Saad Eddin S., Suriajaya A.I.: Stieltjes constants of $L$-functions in the extended Selberg class. In: Ramanujan J., 55, pp. 609-621, 2021. DOI:10.1007/s11139-021-00391-1
  13. Serdyuk A., Stepaniuk T.: Asymptotically best possible Lebesque-type inequalities for the Fourier sums on sets of generalized Poisson integrals, In: Filomat, to appear. arXiv:1908.09517.
  14. Hinrichs A., Krieg D., Novak E., Prochno J., Ullrich M.: Random sections of ellipsoids and the power of random information. In: Transactions of the AMS 374 (2021), no. 12, pp. 8691-8713Link.
  15. Krieg D., Ullrich M.: Function values are enough for $L_2$-approximation. In: Foundations of Computational Mathematics 21 (2021), no. 4, pp. 1141-1151Link.
  16. Krieg D., Ullrich M.: Function values are enough for $L_2$-approximation: Part II. In: J. Complexity 66 (2021), no. 101569, p.14. Link.
  17. Grabner P. J.: Purity results for some arithmetically defined measures, Submitted, 2019. arXiv:1908.09023.
  18. Johnston S., Prochno J.: A Maxwell principle for generalized Orlicz balls, Submitted, 2020. arXiv:2012.11568.
  19. 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.
  20. Ebert A., Kritzer P., Nuyens D., Osisiogu O.: Digit-by-digit and component-by-component constructions of lattice rules for periodic functions with unknown smoothness. In: J. Complexity 66, 101555, 2021.   arXiv:2001.02978v1 
  21. Serdyuk A.S., Stepanyuk T.: Uniform approximations by Fourier sums on classes of convolutions of periodic functions, Submitted, 2020. arXiv:2001.00374v1
  22. Wiart, J., Wong, E.: An application of symbolic computation to quasi-Monte Carlo integration. In: Mathematics and Computers in Simulation, Bd. 182, S. 277-295, 2021. arXiv:2006.06225v1
  23. Desmettre S., Wahl M., Zagst R.: Dynamic Surplus Optimization with Performance- and Index-Linked Liabilities, In: European Actuarial Journal (online), 2021. DOI:10.1007/s13385-021-00292-z.
  24. Kaltenböck L., Kiuchi I., Saad Eddin S. and Ueda M.: Sums of averages of gcd-sum functions II, In: Results in Mathematics, 76(43), 2021. DOI: 10.1007/s00025-021-01357-x.
  25. Kiuchi I. and Saad Eddin S.: On the weighted average number of subgroups of ${\mathbb {Z}}_{m}\times {\mathbb {Z}}_{n}$ with $mn\leq x$. In: Int. J. Number Theory, to appear. arXiv:2008.07850.
  26. Ebert A., Kritzer P., Osisiogu O., Stepaniuk T.: Component-by-component digit-by-digit construction of good polynomial lattice rules in weighted Walsh spaces. In: Constr. Approx., to appear. arXiv:2008.08966
  27. Hofer R.: Finding both, the continued fraction and the Laurent series expansion of golden ratio analogs in the field of formal power series. In: Journal of Number Theory, 223, pp. 168-194, 2021. arXiv:2008.04518
  28. Kritzer P., Pillichshammer F., Wasilkowski G.W.: On quasi Monte Carlo methods in weighted ANOVA spaces, In: Mathematics of Computation 90, 1381--1406, 2021. arXiv:2001.05765
  29. Pillichshammer F.: A note on Korobov lattice rules for integration of analytic functions, In: J. Complexity, 63,101524, 2021. arXiv:2010.03286
  30. Sonnleitner M., Pillichshammer F.: On the relation of the spectral test to isotropic discrepancy and $L_q$-approximation in Sobolev spaces. In: J. Complexity, 67: 101576, 9 pp., 2021. arXiv:2010.04522.
  31. Desmettre S., Leobacher G., Rogers L.C.G.: Change of drift in one-dimensional diffusions, In: Finance and Stochastics, 25(2), pp. 359-381, 2021. https://doi.org/10.1007/s00780-021-00451-w.
  32. Hinrichs A., Kritzinger R., Pillichshammer F.: Extreme and periodic $L_2$ discrepancy of plane point sets, In: Acta Arith., 199(2), pp. 163-198, 2021. arXiv:2005.09933.
  33. Drmota M., Mauduit C., Rivat J., Spiegelhofer L.: Möbius orthogonality for sequences with maximal entropy, In: J. Anal. Math., to appear. arXiv:2001.07898.
  34. Spiegelhofer L.: A lower bound for Cusick's conjecture on the digits of n+t, In: Math. Proc. Cambridge Philos. Soc., to appear. arXiv:1910.13170.
  35. Spiegelhofer L.: The level of distribution of the Thue--Morse sequence, In: Compos. Math., to appear. arXiv:1803.01689.
  36. Amri M., Spiegelhofer L., Thuswaldner J.: Sur la répartition jointe de la représentation d'Ostrowski dans les classes de résidu, Submitted. arXiv:2006.06960.
  37. Spiegelhofer L., Wallner M.: The digits of n+t, Submitted. arXiv:2005.07167.
  38. Adamczewski B., Drmota M., Müllner C.: (Logarithmic) densities for automatic sequences along primes and squares. In: Transactions AMS, to appear. arXiv:2009.14773.
  39. Gillibert P., Lachmann T., Müllner C.: The VC-Dimension of Axis-Parallel Boxes on the Torus. In: Journal of Complexity. Link: The VC-dimension of axis-parallel boxes on the Torus - ScienceDirect. 2022. arXiv:2004.13861.
  40. Drmota M., Verwee J.: Effective Erdos-Wintner Theorems for Digital Expansions. In: Journal of Number Theory, to appear. arXiv:2009.05435.
  41. Aistleitner C., Technau N., Zafeiropoulos A.: On the order of magnitude of Sudler products, Submitted. arXiv:2002.06602.
  42. Aistleitner C., Borda B.: Quantum invariants of hyperbolic knots and extreme values of trigonometric products, Submitted. arXiv:2006.08578.
  43. Aistleiter 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.
  44. Aistleiter C., Baker S., Technau N., Yesha N.: Gap statistics and higher correlations for geometric progressions modulo one, Submitted. arXiv:2010.10355.
  45. Aistleiter C., Gantert N., Kabluchko Z., Prochno J., Ramanan K.: Large Deviation Principles for Lacunary Sums, Submitted. arXiv:2012.05281.
  46. Desmettre S., Wenzel J.: On the Valuation of Discrete Asian Options in High Volatility Environments, Submitted. Link.
  47. Christoph Aistleitner, Thomas Lachmann, Paolo Leonetti, Paolo Minelli: On the number of gaps of sequences with Poissonian Pair Correlations. In: Discrete Mathematics. Link: On the number of gaps of sequences with Poissonian pair correlations - ScienceDirect. 2021. arXiv:1908.06292.
  48. Wilfried Imrich, Thomas Lachmann, Thomas W. Tucker, Gundelinde M. Wiegel, Asymmetrizing cost and density of vertex-transitive cubicgraphs, Submitted. PDF.
  49. Baci A., Kabluchko K., Prochno J., Sonnleitner M., Thäle Ch.: Limit theorems for random points in a simplex, Submitted. arXiv:2005.04911.
  50. Hinrichs A., Prochno J., Vybiral J.: Gelfand numbers of embeddings of Schatten classes. In: Mathematische Annalen 380 (2021), no. 3-4, pp. 1563-1593. Link
  51. 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.
  52. Krieg D., Sonnleitner M.: Random points are optimal for the approximation of Sobolev functions, Submitted. arXiv:2009.11275.
  53. Ebert A., Kritzer P., Osisiogu O., Stepaniuk T.: Construction of good polynomial lattice rules in weighted Walshspaces by an alternative component-by-component construction, In: Math. Comp. Sim. 192, pp 399-419, 2022. arXiv:2101.12586.
  54. Tichy R., Vukusic I., Yang D., Ziegler V.: Integers representable as differences of linear recurrence sequences, Submitted. arXiv:2008.00844.
  55. Ddamulira M., Luca F.: On the exponential Diophantine equation related to powers of two consecutive terms of Lucas sequences. In: Ramanujan J., to appear. https://doi.org/10.1007/s11139-020-00278-7
  56. Ddamulira M.: Padovan numbers that are concatenations of two distinct repdigits. In. Math. Slovaca, to appear. arXiv:2003.10705.
  57. Ebert A., Pillichshammer F.: Tractability of approximation in the weighted Korobov space in the worst-case setting -- a complete picture. In: J. Complexity, 67: 101571, 15pp., 2021. arXiv:2102.01449.
  58. Kritzinger R., Wiart J.: Improved dispersion bounds for modified Fibonacci lattices. In: J. Complexity, 63, 14 pp., 2021. arXiv:2007.02297.
  59. Kritzinger R.: Dispersion of digital (0,m,2) nets. In: Monatshefte für Mathematik, 195(1), pp. 155-171, 2021. arXiv:2004.14760.
  60. Kiuchi I., Saad Eddin S.: On sums of arithmetic functions involving the greatest common divisor, Submitted, 2021. arXiv:2102.03714.
  61. Dick J., Pillichshammer F.: Weighted integration over a hyperrectangle based on digital nets and sequences. In: J. Comput. Appl. Math., 393: 113509, 25 pp., 2021. arXiv:2009.06993.
  62. Hofer R., Kaltenböck L.: Pair correlations of Halton and Niederreiter Sequences are not Poissonian, in Monatsheft für Mathematik 194, pp. 789-809, 2021. Link.
  63. Desmettre S., Steffensen M.: Optimal Investment with Uncertain Risk Aversion, Submitted, 2021. Link.
  64. Technau M., Zafeiropoulos A.: Metric results on summatory arithmetic functions on Beatty sets. In: Acta Arith., 197(1), pp. 93 - 104, 2021. arXiv:1907.06050.
  65. Pollington A., Velani S., Zafeiropoulos A., Zorin A.: Inhomogeneous Diophantine Approximation on M0-sets with restricted denominators, Submitted, 2019. arXiv:1906.01151.
  66. Neumüller M.: On the asymptotic behaviour of the sine product $\prod_{r=1}^n |2 \sin(\pi r \alpha )|$, Submitted, 2021. arXiv:2103.14307.
  67. Beltrán C., Etayo U., Marzo J., Ortega-Cerdá J.: A sequence of polynomials with optimal condition number. In: J. Amer. Math. Soc., 34(1), pp. 219-244, 2021. doi:10.1090/jams/956.
  68. Bilyk D., Ferizovic D., Glazyrin A., Matzke R., Park J., Vlasiuk O.: Potential Theory with Multivariate Kernels, Submitted, 2021. arXiv:2104.03410.
  69. Brauchart J.S., Grabner P.J.: Weighted $L^2$-norms of Gegenbauer polynomials. manuscript, 2021. arXiv:2103.08303.
  70. 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.
  71. Ferizovic D.: On the $L^2$-norm of Gegenbauer polynomials. In: Math. Sci., to appear, 2021. arXiv:1909.08121.
  72. Grabner P.J.: Asymptotic expansions for the coefficients of extremal quasimodular forms and a conjecture of Kaneko and Koike. In: Ramanujan J., to appear, 2021. arXiv:2007.13569.
  73. Etayo U.: A sharp Bombieri inequality, logarithmic energy and well conditioned polynomials, Submitted. arXiv:1912.05521.
  74. Etayo U.: Spherical cap discrepancy of the Diamond ensemble, Submitted. arXiv:1910.05140.
  75. Heiny J., Johnston S., Prochno J.: Thin-shell theory for rotationally invariant random simplices, Submitted, 2021. arXiv:2103.11872.
  76. Breneis S., Prochno J., Rudolf D.: The minimal spherical dispersion, Submitted, 2021. arXiv:2103.11701.
  77. Johnston S., Kabluchko Z., Prochno J.: Projections of the uniform distribution on the cube - a large deviation perspective, Submitted, 2021. arXiv:2103.16430.
  78. Prochno J., Strzelecki M.: Approximation, Gelfand, and Kolmogorov numbers of Schatten class embeddings, Submitted, 2021. arXiv:2103.13050.
  79. Gómez A.-I., Gómez-Pérez D., and Pillichshammer F.: Secure pseudorandom bit generators and point sets with low star-discrepancy. In: J. Comput. Appl. Math., 396: 113601, 8 pp., 2021. arXiv:2004.14158.
  80. Lemieux Ch. and Wiart J.: On the distribution of scrambled (0,m,s)-nets over unanchored boxes. Submitted, 2021.
  81. Desmettre S., Laudagé C., Sass J.: Scalarized Utility-Based Multi-Asset Risk Measures. Submitted, 2021. Link
  82. Desmettre S., Hochgerner S., Omerovic S., Thonhauser S.: A Mean-Field Extension of the LIBOR Market Model. In: International Journal of Theoretical and Applied Finance. Online, March 5, 2022. doi.org/10.1142/S0219024922500054
  83. Brunhuemer A., Larcher G., Larcher L.: Analysis of Option Trading Strategies Based on the Relation of Implied and Realized S&P500 Volatilities. ACRN Journal of Finance and Risk Perspective, Vol. 10, Special Issue 18th FRAP Conference, pp. 166-203, 2021. Link.
  84. Aichinger F., Desmettre S.: Utility Maximization in Multivariate Volterra Models, Submitted, 2021. arXiv:2111.02191.
  85. Lachmann T., Wiart J.: On the area of empty axis-parallel rectangles amidst 2-dimensional lattice points:, Submited, arXiv:2109.11222.

  86. Kritzinger R., Pillichshammer F.: Exact order of extreme $L_p$ discrepancy of infinite sequences in arbitrary dimension. In: Arch Math., to appear. arXiv:2109.06461.
  87. Kritzinger R., Pillichshammer F.: Point sets with optimal order of extreme and periodic discrepancy. Submitted, 2021. arXiv:2109.05781.
  88. Hinrichs A., Krieg D., Novak E., Vybíral J.: Lower bounds for the error of quadrature formulas for Hilbert spaces. In: J. Complexity 65 (2021), no. 101544, p. 20. Link
  89. Hinrichs A., Krieg D., Novak E., Vybíral J.:  Lower bounds for integration and recovery in L2. To appear in: J. Complexity, . DOI: 10.1016
  90. 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
  91. Gnewuch M., Hefter M., Hinrichs A., Ritter K.: Countable Tensor Products of Hermite Spaces and Spaces of Gaussian Kernels. Submitted, 2021. arXiv:2110.05778
  92. Krieg D., Sonnleitner M.: Function recovery on manifolds using scattered data. Submitted, 2021. arXiv:2109.04106
  93. Krieg D., Novak E., Sonnleitner M.: Recovery of Sobolev functions restricted to iid sampling. To appear. In: Math.ComparXiv:2108.02055
  94. Ebert A., Kritzer P., Pillichshammer F.: Tractability of approximation in the weighted Korobov space in the worst-case setting. Submitted, 2022. arXiv:2201.09940
  95. Larcher G.: Die Black-Scholes-Theorie: In 100 Schritten vom Münzwurf zum Wirtschaftsnobelpreis. Springer-Gabler-Verlag, 2022.
  96. Brunhuemer A., Larcher G.: Quasi-Monte Carlo methods in portfolio selection with many constraints. To appear 2022.
  97. Larcher G.: The exact order of discrepancy for Levin's normal number in base 2. Preprint, 2022. 
  98. Brunhuemer A., Larcher L., Seidl P., Desmettre S., Kofler J., Larcher G.:  Supervised Machine Learning Classification for Short Straddles on the S&P500. Submitted, 2022. arXiv:2204.13587
  99. Krieg D., Siedlecki P., Ullrich M., Woźniakowski H.: Exponential tractability of L2-approximation with function values. Submitted. arXiv:205.04141
  100. Dolbeault M., Krieg D., Ullrich M.: A sharp upper bound for sampling numbers in L2. Submitted. arXiv:220412621
  101. Laudagé C., Sass J., Wenzel J.: Combining multi-asset and intrinsic risk measures, In: Insurance: Mathematics and Economics, Volume 106, September 2022, Pages 254-269, DOI: 10.1016; Link

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. Hickernell, F.J, Kritzer, P. (eds.): Multivariate Algorithms and Information-Based Complexity. DeGruyter, Berlin/Boston, 2020. Link
  2. Dick J., Bilyk D., and Pillichshammer F. (eds.): Discrepancy Theory, De Gruyter, Berlin, 2020. ISBN: 978-3-11-065115-7
  3. 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.