On the discrepancy of two-dimensional perturbed Halton--Kronecker sequences and lacunary trigonometric products
نویسندگان
چکیده
منابع مشابه
Sharp General and Metric Bounds for the Star Discrepancy of Perturbed Halton–kronecker Sequences
We consider distribution properties of two-dimensional hybrid sequences (zk)k in the unit square of the form zk = ({kα}, xk), where α ∈ (0, 1) is irrational and (xk)k denotes a digital Niederreiter sequence. By definition, the construction of the sequence (xk)k relies on an infinite matrix C with entries in {0, 1}. Two special cases of such matrices were studied by Niederreiter (2009) and by Ai...
متن کاملImproved Halton sequences and discrepancy bounds
For about fifteen years, the surprising success of quasi-Monte Carlo methods in finance has been raising questions that challenge our understanding of these methods. At the origin are numerical experiments performed with so-called GSobol’ and GFaure sequences by J. Traub and his team at Columbia University, following the pioneering work of S. Tezuka in 1993 on generalizations of Niederreiter (t...
متن کاملOn Lacunary Trigonometric Series.
1. Fundamental theorem. In a recent paper f I have proved the theorem that if a lacunary trigonometric series CO (1) X(a* cos nk6 + bk sin nk9) (nk+x/nk > q > 1, 0 ^ 0 ^ 2ir) 4-1 has its partial sums uniformly bounded on a set of 0 of positive measure, then the series (2) ¿(a*2 + bk2) k-l converges. The proof was based on the following lemma (which was not stated explicitly but is contained in ...
متن کاملThe Discrepancy of Generalized Van-der-corput-halton Sequences
The purpose of this paper is to provide upper bounds for the discrepancy of generalized Van-der-Corput-Halton sequences that are built from Halton sequences and the Zeckendorf Van-der-Corput sequence.
متن کاملLacunary Trigonometric Series. Ii
where E c [0, 1] is any given set o f positive measure and {ak} any given sequence of real numbers. This theorem was first proved by R. Salem and A. Zygmund in case of a -0, where {flk} satisfies the so-called Hadamard's gap condition (cf. [4], (5.5), pp. 264-268). In that case they also remarked that under the hypothesis (1.2) the condition (1.3) is necessary for the validity of (1.5) (cf. [4]...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 2017
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa170505-6-7