Optimal error bound of restricted Monte Carlo integration on anisotropic Sobolev classes

DOI10.1080/10020070612330039zbMath1129.65002OpenAlexW2086845637MaRDI QIDQ2455840

Yanyan Li

Publication date: 26 October 2007

Published in: Progress in Natural Science (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/10020070612330039

zbMATH Keywords

discretization techniquehigh-dimensional integralsanisotropic Sobolev classesrandom bitsrandomized \((n,m)\)-th minimal errorrestricted Monte Carlo integrationrestricted randomized algorithms

Mathematics Subject Classification ID

Monte Carlo methods (65C05) Well-distributed sequences and other variations (11K36) Stochastic particle methods (65C35) Pseudo-random numbers; Monte Carlo methods (11K45)

Related Items (6)

Randomized complexity of parametric integration and the role of adaption. II: Sobolev spaces ⋮ Lower Bounds for the Number of Random Bits in Monte Carlo Algorithms ⋮ On the Power of Restricted Monte Carlo Algorithms ⋮ Random bit quadrature and approximation of distributions on Hilbert spaces ⋮ Optimal integration error on anisotropic classes for restricted Monte Carlo and quantum algorithms ⋮ Random bit multilevel algorithms for stochastic differential equations

This page was built for publication: Optimal error bound of restricted Monte Carlo integration on anisotropic Sobolev classes