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arXiv · 1611.01288

Sharp general and metric bounds for the star discrepancy of perturbed Halton--Kronecker sequences

Roswitha Hofer·Florian Puchhammer
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Abstract

We consider the star discrepancy of two-dimensional sequences made up as a hybrid between a Kronecker sequence and a perturbed Halton sequence in base 2, where the perturbation is achieved by a digital-sequence construction in the sense of Niederreiter whose generating matrix contains a periodic perturbing sequence of a given period length. Under the assumption that the Kronecker sequence involves a parameter with bounded continued fraction coefficients sharp discrepancy estimates are obtained. Furthermore, we study the problem from a metric point of view as well. Finally, we also present sharp general and tight metric bounds for certain lacunary trigonometric products which appear to be strongly related to these problems.

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Roswitha Hofer, Florian Puchhammer. 2016-11-04. Sharp general and metric bounds for the star discrepancy of perturbed Halton--Kronecker sequences. https://doi.org/10.4064/aa170505-6-7

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