Discrepancy of higher rank polynomial lattice point sets

Greslehner Julia () and Pillichshammer Friedrich ()
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Greslehner Julia: Institut für Finanzmathematik, Universität Linz, Altenbergerstr. 69, 4040 Linz, Austria
Pillichshammer Friedrich: Institut für Finanzmathematik, Universität Linz, Altenbergerstr. 69, 4040 Linz, Austria

Monte Carlo Methods and Applications, 2012, vol. 18, issue 1, 79-108

Abstract: Polynomial lattice point sets (PLPSs) (of rank 1) are special constructions of finite point sets which may have outstanding equidistribution properties. Such point sets are usually required as nodes in quasi-Monte Carlo rules. Any PLPS is a special instance of a -net in base as introduced by Niederreiter. In this paper we generalize PLPSs of rank 1 to what we call then PLPSs of rank and analyze their equidistribution properties in terms of the quality parameter and the (weighted) star discrepancy. We show the existence of PLPSs of “good” quality with respect to these quality measures. In case of the (weighted) star discrepancy such PLPSs can be constructed component-by-component wise. All results are for PLPSs in prime power base . Therefore, we also generalize results for PLPSs of rank 1 that were only known for prime bases so far.

Keywords: Discrepancy; polynomial lattice point set; digital nets (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1515/mcma-2012-0001

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