## Note on “The smoothing effect of integration in $\mathbb {R}^d$ and the ANOVA decomposition”

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- by Michael Griebel, Frances Y. Kuo and Ian H. Sloan PDF
- Math. Comp.
**86**(2017), 1847-1854 Request permission

## Abstract:

This is a note on Math. Comp.**82**(2013), 383–400. 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 assumption (3.3) in the theorem is not satisfied by the Asian option pricing problem. In this note we present a strengthened theorem, which removes that assumption. The new theorem is immediately applicable to the Asian option pricing problem with the standard and Brownian bridge constructions. Thus the option pricing conclusions of our original paper stand.

## References

- Milton Abramowitz and Irene A. Stegun (eds.),
*Handbook of mathematical functions with formulas, graphs, and mathematical tables*, Dover Publications, Inc., New York, 1992. Reprint of the 1972 edition. MR**1225604** - Robert A. Adams,
*Sobolev spaces*, Pure and Applied Mathematics, Vol. 65, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1975. MR**0450957** - Michael Griebel, Frances Y. Kuo, and Ian H. Sloan,
*The smoothing effect of integration in $\Bbb {R}^d$ and the ANOVA decomposition*, Math. Comp.**82**(2013), no. 281, 383–400. MR**2983028**, DOI 10.1090/S0025-5718-2012-02578-6

## Additional Information

**Michael Griebel**- Affiliation: Institut für Numerische Simulation, Universität Bonn, Wegelerstrasse 6, 53115, Bonn, Germany – and – Fraunhofer Institute for Algorithms and Scientific Computing SCAI, Schloss Birlinghoven, 53754 Sankt Augustin, Germany
- MR Author ID: 270664
- Email: griebel@ins.uni-bonn.de
**Frances Y. Kuo**- Affiliation: School of Mathematics and Statistics, University of New South Wales, Sydney, New South Wales 2052, Australia
- MR Author ID: 703418
- Email: f.kuo@unsw.edu.au
**Ian H. Sloan**- Affiliation: School of Mathematics and Statistics, University of New South Wales, Sydney, New South Wales 2052, Australia
- MR Author ID: 163675
- ORCID: 0000-0003-3769-0538
- Email: i.sloan@unsw.edu.au
- Received by editor(s): June 23, 2015
- Received by editor(s) in revised form: November 29, 2015
- Published electronically: October 7, 2016
- © Copyright 2016 American Mathematical Society
- Journal: Math. Comp.
**86**(2017), 1847-1854 - MSC (2010): Primary 41A63, 41A99; Secondary 65D30
- DOI: https://doi.org/10.1090/mcom/3172
- MathSciNet review: 3626539