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ON HYBRID SEQUENCES BUILT FROM NIEDERREITER–HALTON SEQUENCES AND KRONECKER SEQUENCES

Part of: Probabilistic theory: distribution modulo $1$; metric theory of algorithms

Published online by Cambridge University Press:  29 July 2011

ROSWITHA HOFER  and
PETER KRITZER
ROSWITHA HOFER
Affiliation:
Institut für Finanzmathematik, Universität Linz, Altenbergerstr. 69, 4040 Linz, Austria (email: roswitha.hofer@jku.at)
PETER KRITZER*
Affiliation:
Institut für Finanzmathematik, Universität Linz, Altenbergerstr. 69, 4040 Linz, Austria (email: peter.kritzer@jku.at)
*
✉For correspondence; e-mail: peter.kritzer@jku.at
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Abstract

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We discuss the distribution properties of hybrid sequences whose components stem from Niederreiter–Halton sequences on the one hand, and Kronecker sequences on the other. In this paper, we give necessary and sufficient conditions on the uniform distribution of such sequences, and derive a result regarding their discrepancy. We conclude with a short summary and a discussion of topics for future research.

Keywords

uniform distribution modulo onediscrepancyKronecker sequenceNiederreiter–Halton sequence

MSC classification

Secondary: 11K06: General theory of distribution modulo $1$ 11K38: Irregularities of distribution, discrepancy
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 84 , Issue 2 , October 2011 , pp. 238 - 254
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2011

Footnotes

The authors gratefully acknowledge the support of the Austrian Science Fund (Project P21943).

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