Lp- and Sp,qrB-discrepancy of (order 2) digital nets

DOI10.4064/aa168-2-4zbMath1328.11083arXiv1402.4424OpenAlexW3100745717MaRDI QIDQ5246951

Lev Markhasin

Publication date: 22 April 2015

Published in: Acta Arithmetica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1402.4424

zbMATH Keywords

Walsh systemHaar systemquasi-Monte Carlodominating mixed smoothness\(L_p\)-discrepancyorder 2 digital nets

Mathematics Subject Classification ID

Monte Carlo methods (65C05) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) (42C10) Irregularities of distribution, discrepancy (11K38) General theory of distribution modulo (1) (11K06)

Related Items (10)

Optimal quasi-Monte Carlo rules on order 2 digital nets for the numerical integration of multivariate periodic functions ⋮ On the upper bound of the $L_2$-discrepancy of Halton’s sequence ⋮ BMO and exponential Orlicz space estimates of the discrepancy function in arbitrary dimension ⋮ Optimal \(L_{p}\)-discrepancy bounds for second order digital sequences ⋮ Point sets with optimal order of extreme and periodic discrepancy ⋮ The curse of dimensionality for the \(L_p\)-discrepancy with finite \(p\) ⋮ Central limit theorem for \((t,s)\)-sequences in base 2 ⋮ DISCREPANCY OF SECOND ORDER DIGITAL SEQUENCES IN FUNCTION SPACES WITH DOMINATING MIXED SMOOTHNESS ⋮ Discrepancy of Digital Sequences: New Results on a Classical QMC Topic ⋮ Exact order of extreme \(L_p\) discrepancy of infinite sequences in arbitrary dimension

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