@article {IOPORT.05798211,
    author       = {Griebel, Michael and Kuo, Frances Y. and Sloan, Ian H.},
    title        = {The smoothing effect of the ANOVA decomposition.},
    year         = {2010},
    journal      = {Journal of Complexity},
    volume       = {26},
    number       = {5},
    issn         = {0885-064X},
    pages        = {523-551},
    publisher    = {Elsevier Science (Academic Press), San Diego, CA},
    doi          = {10.1016/j.jco.2010.04.003},
    abstract     = {ANOVA decomposition of a multivariate function became an important tool in understanding high dimensional functions on one hand and the success of the quasi Monte Carlo or sparse grid techniques when implementing high dimensional integration problems. It is shown that the lower order terms in the considered ANOVA decomposition of the function~$f$ may be smoother than~$f$ itself. Pricing an arithmetic Asian option on a single stock with~$d$ time intervals serves throughout the papers and basic practical motivation. The paper is organized as follows. In Section~2 all necessary background information about the ANOVA decomposition and on different Sobolev spaces, and state simple properties for functions with bounded mixed derivatives are given. In Section~3 a family of functions with kink of option prices is presented and smoothness properties of the ANOVA terms derived. Section~4 deals with the more extreme case of functions with a jump. In Section~5 some option price problems are considered as example. Numerical aspects are concisely summarized in Section~6. Finally, concluding remarks can be found in Section~7.},
    reviewer     = {Jaromir Antoch (Praha)},
    identifier   = {05798211},
}