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Scrambled Polynomial Lattice Rules for Infinite-Dimensional Integration

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Monte Carlo and Quasi-Monte Carlo Methods 2010

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 23))

Abstract

In the random case setting, scrambled polynomial lattice rules, as discussed in Baldeaux and Dick (Numer. Math. 119:271–297, 2011), enjoy more favorable strong tractability properties than scrambled digital nets. This short note discusses the application of scrambled polynomial lattice rules to infinite-dimensional integration. In Hickernell et al. (J Complex 26:229–254, 2010), infinite-dimensional integration in the random case setting was examined in detail, and results based on scrambled digital nets were presented. Exploiting these improved strong tractability properties of scrambled polynomial lattice rules and making use of the analysis presented in Hickernell et al. (J Complex 26:229–254, 2010), we improve on the results that were achieved using scrambled digital nets.

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Authors and Affiliations

  1. School of Finance and Economics, University of Technology, Sydney, NSW, Australia

    Jan Baldeaux

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  1. Jan Baldeaux
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Correspondence to Jan Baldeaux .

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Editors and Affiliations

  1. , Institute of Applied Mathematics, University of Warsaw, Banacha 2, Warsaw, 02-097, Poland

    Leszek Plaskota

  2. , Institute of Applied Mathematics, University of Warsaw, Banacha 2, Warsaw, 02-097, Poland

    Henryk Woźniakowski

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Baldeaux, J. (2012). Scrambled Polynomial Lattice Rules for Infinite-Dimensional Integration. In: Plaskota, L., Woźniakowski, H. (eds) Monte Carlo and Quasi-Monte Carlo Methods 2010. Springer Proceedings in Mathematics & Statistics, vol 23. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27440-4_11

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