Probabilistic diophantine approximation and the distribution of Halton-Kronecker sequences

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• 作者：Gerhard Larcher
• 关键词：Uniform distribution of sequences ; Discrepancy ; Diophantine approximation ; Kronecker sequences ; Halton sequences
• 刊名：Journal of Complexity
• 出版年：2013
• 出版时间：December, 2013
• 年：2013
• 卷：29
• 期：6
• 页码：397-423
• 全文大小：483 K

文摘

By a Halton-Kronecker sequence we mean a sequence in the -dimensional unit-cube which is the combination of an -dimensional Halton sequence and a -dimensional Kronecker sequence with . The investigation of such ¡®hybrid sequences¡¯ for their use in Monte Carlo and quasi-Monte Carlo methods first was motivated by Spanier (1995) . By suitably adapting techniques of Jozsef Beck on probabilistic diophantine approximation, developed in Beck (1994) , we can show that for almost all for the discrepancy of a Halton-Kronecker sequence we have for all , which most probably essentially is the best possible metrical result for this type of sequences.