Work

Randomized quasi-Monte Carlo and Owen’s boundary growth condition: a spectral analysis

Year: 2025

Type: article

Abstract: In this work we analyse the convergence rate of randomized quasi-Monte Carlo (RQMC) methods under Owen’s boundary growth condition (Owen, A. B. (2006) Halton sequences avoid the origin. SIAM Rev., 48, 487−503.) via spectral analysis. Specifically, we examine the RQMC estimator variance for the two commonly studied sequences: the lattice rule and the Sobol’ sequence. We apply the Fourier transform and Walsh–Fourier transform, respectively. Assuming certain regularity conditions our findings reveal that the asymptotic convergence rate of the RQMC estimator’s variance closely aligns with the exponent specified in Owen’s boundary growth condition for both sequence types. We also provide analysis for certain discontinuous integrands.

Source: IMA Journal of Numerical Analysis

DOI: 10.1093/imanum/draf020

Author: Yang Liu

Institution: King Abdullah University of Science and Technology

Language: English

Topic: Mathematical Approximation and Integration

Subfield: Numerical Analysis

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Alexander von Humboldt-Stiftung, King Abdullah University of Science and Technology

Award: G1170852293