Error bounds for quasi-Monte Carlo integration for \mathscrL^∞ with uniform point sets

2010/05/31 by Su Hu, Yan Li, Hu, Su +1
Mathematics · #FOS: Mathematics #Mathematical Approximation and Integration #Number Theory (math.NT) #Numerical Analysis (math.NA) #Primary 11K45 #Secondary 65D30

paper · pdf · doi:10.48550/arxiv.1005.5575

openalex publication_date 2010/05/31 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

Abstract

Niederreiter [H.Niederreiter, Error bounds for quasi-Monte Carlo integration with uniform point sets, Journal of computational and applied mathematics 150 (2003), 283-292] established new bounds for quasi-Monte Carlo integration for nodes sets with a special kind of uniformity property. Let (X,\mathscrA,μ) be an arbitrary probability space, i.e., X is an arbitrary nonempty set, \mathscrA a σ-algebra of subsets of X, and μa probability measure defined on \mathscrA. The functions considered in Niederreiter's paper are bounded μ-integrable functions on X. In this note, we extend some of his results for bounded μ-integrable functions to essentially bounded \mathscrA-measurable functions. So Niederreiter's bounds can be used in a more general setting.

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