Scrambled polynomial lattice rules for infinite-dimensional integration

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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