$L^p$-discrepancy and statistical independence of sequences

Peter J. Grabner; Oto Strauch; Robert Franz Tichy

Displaying similar documents to “ $L^{p}$ -discrepancy and statistical independence of sequences”

A generalization of NUT digital (0,1)-sequences and best possible lower bounds for star discrepancy

Henri Faure, Friedrich Pillichshammer (2013)

Acta Arithmetica

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In uniform distribution theory, discrepancy is a quantitative measure for the irregularity of distribution of a sequence modulo one. At the moment the concept of digital (t,s)-sequences as introduced by Niederreiter provides the most powerful constructions of s-dimensional sequences with low discrepancy. In one dimension, recently Faure proved exact formulas for different notions of discrepancy for the subclass of NUT digital (0,1)-sequences. It is the aim of this paper to generalize...

Some metric properties of subsequences

Pierre Liardet (1990)

Acta Arithmetica

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On existence and discrepancy of certain digital Niederreiter-Halton sequences

Roswitha Hofer, Gerhard Larcher (2010)

Acta Arithmetica

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An improved result on irregularities in distribution of sequences of integers

John H. Hodges (1988)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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In 1972 the author used a result of K.F. Roth on irregularities in distribution of sequences of real numbers to prove an analogous result related to the distribution of sequences of integers in prescribed residue classes. Here, a 1972 result of W.M. Schmidt, which is an improvement of Roth's result, is used to obtain an improved result for sequences of integers.

An improved result on irregularities in distribution of sequences of integers

John H. Hodges (1988)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

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σ-asymptotically lacunary statistical equivalent sequences

Ekrem Savaş, Richard Patterson (2006)

Open Mathematics

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This paper presents the following definitions which is a natural combination of the definition for asymptotically equivalent, statistically limit, lacunary sequences, and σ-convergence. Let ϑ be a lacunary sequence; Two nonnegative sequences [x] and [y] are S σ,8-asymptotically equivalent of multiple L provided that for every ε > 0 $lim_{r} \frac{1}{h_{r}} \{k \in I_{r} : |\frac{x_{σ^{k} (m)}}{y_{σ^{k} (m)}} - L| ⩾ \in\} = 0$ uniformly in m = 1, 2, 3, ..., (denoted by x $\overset{S_{σ, θ}}{\sim}$ y) simply S σ,8-asymptotically equivalent, if L = 1. Using this definition we shall prove S σ,8-asymptotically...