Discrepancy of randomly sampled sequences of reals

被引：9

作者：

Weber, M

机构：

[1] Univ Strasbourg 1, IRMA, F-67084 Strasbourg, France

[2] CNRS, F-67084 Strasbourg, France

来源：

MATHEMATISCHE NACHRICHTEN | 2004年 / 271卷

关键词：

metric entropy method; diophantine approximation; sampled subsequences; i.i.d; sums; discrepancy;

D O I：

10.1002/mana.200310184

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We estimate the discrepancy of (nx) when n is sampled by a random walk and give examples involving the diophantine approximation properties of x. The proof relies upon the combination of the metric entropy method and the Erdos-Turan inequality. (C) 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

引用

页码：105 / 110

页数：6

共 13 条

[1] ON SUM SIGMA [NALPHA]-T AND NUMERICAL INTEGRATION [J].

HABER, S ;

OSGOOD, CF .

PACIFIC JOURNAL OF MATHEMATICS, 1969, 31 (02) :383-&

[2]

HARMAN G, 1988, LONDON MATH SOC MONO

[3]

HOLEWIJN PJ, 1973, Z WAHRSCHEINLICHKEIT, V26, P33

[4]

Kawata T., 1972, Fourier analysis in probability theory

[5]

Kesten, 1965, ACTA ARITH, V10, P183, DOI DOI 10.4064/AA-10-2-183-213

[6]

KUIPERS L, 1974, UNIFORM DISTRIBUTION

[7]

ROBBINS H, 1973, P AM MATH SOC, V4, P786

[8] ON THE ASYMPTOTIC UNIFORM-DISTRIBUTION OF SUMS REDUCED MOD-1 [J].

SCHATTE, P .

MATHEMATISCHE NACHRICHTEN, 1984, 115 :275-281

[9]

SCHATTE P, COMMUNICATION

[10]

SCHATTE P, 1988, PROBAB THEORY REL, V4, P167

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