Fachgruppe Mathematik: Browsing Fachgruppe Mathematik by Author "Kuo, Frances Y."
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Note on “The smooting effect of integration in ℝd and the ANOVA decomposition”
Griebel, Michael; Kuo, Frances Y.; Sloan, Ian H. (2015)This is a note on [Math. Comp. <b>82</b>, 383–400 (2013)]. We first report a mistake, in that the main result Theorem 3.1, though correct, does not as claimed apply to the Asian option pricing problem. This is because ... -
On the expected uniform error of Brownian motion approximated by the Lévy-Ciesielski construction
Brown, Bruce; Griebel, Michael; Kuo, Frances Y.; Sloan, Ian H. (2023-04)It is known that the Brownian bridge or Lévy-Ciesielski construction of Brownian paths almost surely converges uniformly to the true Brownian path. In the present article the focus is on the uniform error. In particular, ... -
On the expected uniform error of geometric Brownian motion approximated by the Lévy-Ciesielski construction
Brown, Bruce; Griebel, Michael; Kuo, Frances Y.; Sloan, Ian H. (2017-06)It is known that the Brownian bridge or Lévy-Ciesielski construction of Brownian paths almost surely converges uniformly to the true Brownian path. In the present article the focus is on the error. In particular, we show ... -
The ANOVA decomposition of a non-smooth function of infinitely many variables can have every term smooth
Griebel, Michael; Kuo, Frances Y.; Sloan, Ian H. (2014)The pricing problem for a continuous path-dependent option results in a path integral which can be recast into an infinite-dimensional integration problem. We study ANOVA decomposition of a function of infinitely many ... -
The smoothing effect of integration in ℝd and the ANOVA decomposition
Griebel, Michael; Kuo, Frances Y.; Sloan, Ian H. (2010-12)This paper studies the ANOVA decomposition of a <em>d</em>-variate function <em>f</em> defined on the whole of ℝ<em><sup>d</sup></em>, where <em>f</em> is the maximum of a smooth function and zero (or <em>f</em> could ...