Robust Faber–Schauder Approximation Based on Discrete Observations of an Antiderivative

Published Online:https://doi.org/10.1287/moor.2022.0328

References

  • [1] Allaart PC, Kawamura K (2011) The Takagi function: A survey. Real Anal. Exchange 37(1):1–54.CrossrefGoogle Scholar
  • [2] Bayraktar E, Das P, Kim D (2025) Hölder regularity and roughness: Construction and examples. Bernoulli 31(2):1084–1113.CrossrefGoogle Scholar
  • [3] Ciesielski Z (1960) On the isomorphisms of the spaces hα and m. Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 8:217–222.Google Scholar
  • [4] Ciesielski Z (1993) Quelques espaces fonctionnels associés à des processus gaussiens. Studia Math. 107(2):171–204.CrossrefGoogle Scholar
  • [5] Cont R, Das P (2022) Quadratic variation along refining partitions: Constructions and examples. J. Math. Anal. Appl. 512(2):126173.CrossrefGoogle Scholar
  • [6] Cont R, Das P (2024) Rough volatility: Fact or artefact? Sankhya B 86(1):191–223.CrossrefGoogle Scholar
  • [7] Devroye L (1987) A Course in Density Estimation (Birkhauser Boston Inc., Cambridge, MA).Google Scholar
  • [8] Fukasawa M, Takabatake T (2019) Asymptotically efficient estimators for self-similar stationary Gaussian noises under high frequency observations. Bernoulli 25(3):1870–1900.CrossrefGoogle Scholar
  • [9] Gatheral J, Jaisson T, Rosenbaum M (2018) Volatility is rough. Quant. Finance 18(6):933–949.CrossrefGoogle Scholar
  • [10] Halmos PR (2012) A Hilbert Space Problem Book, Graduate Texts in Mathematics, vol. 19 (Springer Science & Business Media, New York).Google Scholar
  • [11] Han X, Schied A (2023) Estimating the roughness exponent of stochastic volatility from discrete observations of the integrated variance. Preprint, submitted August 9, https://arxiv.org/abs/2307.02582.Google Scholar
  • [12] Han X, Schied A (2025) The roughness exponent and its model-free estimation. Ann. Appl. Probab. 35(2):1049–1082.CrossrefGoogle Scholar
  • [13] Hata M, Yamaguti M (1984) The Takagi function and its generalization. Japan J. Appl. Math. 1(1):183–199.CrossrefGoogle Scholar
  • [14] Ingtem J (2008) Minimal-norm-derivative spline function in interpolation and approximation. Moscow Univ. Comput. Math. Cybernetics 32(4):201–213.CrossrefGoogle Scholar
  • [15] Izenman AJ (1991) Recent developments in nonparametric density estimation. J. Amer. Statist. Assoc. 86(413):205–224.Google Scholar
  • [16] Lagarias JC (2012) The Takagi function and its properties. Matsumoto K, Akiyama S, Fukuyama K, Nakada H, Sugita H, Tamagawa A, eds. Functions in Number Theory and Their Probabilistic Aspects, RIMS Kôkyûroku Bessatsu, B34 (Research Institute for Mathematical Sciences, Kyoto University, Kyoto, Japan), 153–189.Google Scholar
  • [17] Losonczi L (1992) Eigenvalues and eigenvectors of some tridiagonal matrices. Acta Math. Hung. 60(3–4):309–322.CrossrefGoogle Scholar
  • [18] Matveev VA (1967) Series in a Schauder system. Matematicheskie Zametki 2(3):267–278.Google Scholar
  • [19] Mettke H, Pfeifer E, Neuman E (1982) Quadratic spline interpolation with coinciding interpolation and spline grids. J. Comput. Appl. Math. 8(1):57–62.CrossrefGoogle Scholar
  • [20] Wee A, Grayden DB, Zhu Y, Petkovic‐Duran K, Smith D (2008) A continuous wavelet transform algorithm for peak detection. Electrophoresis 29(20):4215–4225. CrossrefGoogle Scholar
INFORMS site uses cookies to store information on your computer. Some are essential to make our site work; Others help us improve the user experience. By using this site, you consent to the placement of these cookies. Please read our Privacy Statement to learn more.