Asymptotic behavior of average \(L_p\)-discrepancies

DOI10.1016/j.jco.2012.04.003zbMath1268.11101OpenAlexW2201413591MaRDI QIDQ432762

Heidi Weyhausen, Aicke Hinrichs

Publication date: 4 July 2012

Published in: Journal of Complexity (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jco.2012.04.003

zbMATH Keywords

quasi-Monte Carlo methodsstar discrepancyuniform distribution theoryaverage discrepancy

Mathematics Subject Classification ID

Random number generation in numerical analysis (65C10) Irregularities of distribution, discrepancy (11K38) Pseudo-random numbers; Monte Carlo methods (11K45)

Related Items (7)

A note on the periodic \(L_2\)-discrepancy of Korobov's \(p\)-sets ⋮ Optimal periodic \(L_2\)-discrepancy and diaphony bounds for higher order digital sequences ⋮ Extreme and periodic $L_2$ discrepancy of plane point sets ⋮ A lower bound for the discrepancy of a random point set ⋮ Measures of uniformity in experimental designs: A selective overview ⋮ Calculation of Discrepancy Measures and Applications ⋮ Proof techniques in quasi-Monte Carlo theory

Cites Work

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• Covering numbers, dyadic chaining and discrepancy
• Weighted geometric discrepancies and numerical integration on reproducing kernel Hilbert spaces
• Covering numbers, Vapnik-Červonenkis classes and bounds for the star-discrepancy
• Tractability of multivariate problems. Volume II: Standard information for functionals.
• The asymptotic behavior of the average \(L^p\)-discrepancies and a randomized discrepancy
• Characterization of the law of the iterated logarithm in Banach spaces
• Bounds for the average \(L^p\)-extreme and the \(L^\infty\)-extreme discrepancy
• The inverse of the star-discrepancy depends linearly on the dimension
• Quadrature Errors, Discrepancies, and Their Relations to Halftoning on the Torus and the Sphere

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