$L_p$- and $S_{p,q}^rB$-discrepancy of (order 2) digital nets

• Autorzy: Lev Markhasin
• Języki publikacji: EN

Abstrakty

EN

Dick proved that all dyadic order 2 digital nets satisfy optimal upper bounds on the $L_p$-discrepancy. We prove this for arbitrary prime base b with an alternative technique using Haar bases. Furthermore, we prove that all digital nets satisfy optimal upper bounds on the discrepancy function in Besov spaces with dominating mixed smoothness for a certain parameter range, and enlarge that range for order 2 digital nets. The discrepancy function in Triebel-Lizorkin and Sobolev spaces with dominating mixed smoothness is considered as well.

Kategorie tematyczne

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

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2015
• Tom: 168
• Numer: 2
• Strony: 139-159

Daty

wydano

2015

Twórcy

autor

Lev Markhasin

• Institut für Stochastik und Anwendungen, Universität Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany

Identyfikatory

DOI

10.4064/aa168-2-4