New star discrepancy bounds for -nets and -sequences

被引：0

作者：

Faure, Henri ^{[1
]}

Kritzer, Peter ^{[2
]}

机构：

[1] Univ Aix Marseille, Inst Math Luminy CNRS, F-13288 Marseille 09, France

[2] Univ Linz, Inst Finanzmath, A-4040 Linz, Austria

来源：

MONATSHEFTE FUR MATHEMATIK | 2013年 / 172卷 / 01期

基金：

奥地利科学基金会;

关键词：

Discrepancy; (t; m; s)-net; s)-sequence; Uniform distribution modulo one; 2; DIMENSIONS; (T; S)-SEQUENCES; HAMMERSLEY; SETS;

D O I：

10.1007/s00605-012-0470-1

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we derive new general upper bounds on the star discrepancy of -nets and -sequences. These kinds of point sets are among the most widely used in quasi-Monte Carlo methods for numerical integration. By our new results, we improve on previous discrepancy bounds and prove a conjecture stated by the second author in an earlier paper.

引用

页码：55 / 75

页数：21

共 30 条

[1]

[Anonymous], 1974, PURE APPL MATH

[2]

Atanassov E.I., 2004, MATH BALKANICA, V18, P15

[3] DECREASE OF THE DISCREPANCY OF ANY SERIES ON T [J].

BEJIAN, R .

ACTA ARITHMETICA, 1982, 41 (02) :185-202

[4] On the Small Ball Inequality in all dimensions [J].

Bilyk, Dmitriy ;

Lacey, Michael T. ;

Vagharshakyan, Armen .

JOURNAL OF FUNCTIONAL ANALYSIS, 2008, 254 (09) :2470-2502

[5]

DECLERCK L, 1986, MONATSH MATH, V101, P261, DOI 10.1007/BF01559390

[6] Star discrepancy estimates for digital (t, m, 2)-nets and digital (t, 2)-sequences over Z2 [J].

Dick, J ;

Kritzer, P .

ACTA MATHEMATICA HUNGARICA, 2005, 109 (03) :239-254

[7]

Dick J., 2010, Digital Nets and Sequences: Discrepancy Theory and Quasi-Monte Carlo Integration

[8]

Dick J, 2006, MONTE CARLO METHODS, V12, P1

[9] ON THE STAR-DISCREPANCY OF GENERALIZED HAMMERSLEY SEQUENCES IN 2 DIMENSIONS [J].

FAURE, H .

MONATSHEFTE FUR MATHEMATIK, 1986, 101 (04) :291-300

[10] DISCREPANCY OF SEQUENCES ASSOCIATED WITH A NUMERATION SYSTEM (IN S-DIMENSION) [J].

FAURE, H .

ACTA ARITHMETICA, 1982, 41 (04) :337-351

← 1 2 3 →