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Mathematics > Numerical Analysis

arXiv:2203.17010 (math)
[Submitted on 31 Mar 2022 (v1), last revised 14 Feb 2023 (this version, v3)]

Title:Consistency of randomized integration methods

Authors:Julian Hofstadler, Daniel Rudolf
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Abstract:We prove that a class of randomized integration methods, including averages based on $(t,d)$-sequences, Latin hypercube sampling, Frolov points as well as Cranley-Patterson rotations, consistently estimates expectations of integrable functions. Consistency here refers to convergence in mean and/or convergence in probability of the estimator to the integral of interest. Moreover, we suggest median modified methods and show for integrands in $L^p$ with $p>1$ consistency in terms of almost sure convergence
Comments: 17 pages. Accepted for publication in Journal of Complexity
Subjects: Numerical Analysis (math.NA)
Cite as: arXiv:2203.17010 [math.NA]
  (or arXiv:2203.17010v3 [math.NA] for this version)
  https://doi.org/10.48550/arXiv.2203.17010
Related DOI: https://doi.org/10.1016/j.jco.2023.101740

Submission history

From: Julian Hofstadler [view email]
[v1] Thu, 31 Mar 2022 13:08:22 UTC (11 KB)
[v2] Mon, 10 Oct 2022 15:39:17 UTC (14 KB)
[v3] Tue, 14 Feb 2023 10:54:59 UTC (14 KB)
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