Simplified analysis of randomized quasi-Monte Carlo convergence under boundary growth conditions
Published on:
8 May 2024
Primary Category:
Numerical Analysis
Paper Authors:
Yang Liu
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Key Details
Analyzes RQMC estimator variance decay via spectral analysis
Matches variance decay rates to Owen's boundary growth condition
Examines lattice sequences and Sobol' sequences
Provides guidance on optimizing importance sampling
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Simplified analysis of randomized quasi-Monte Carlo convergence under boundary growth conditions
This paper analyzes the convergence rates of randomized quasi-Monte Carlo methods for integrands that are unbounded near the boundary. Using spectral analysis with Fourier and Walsh-Fourier transforms, the variance decay rates are shown to closely match the boundary growth condition exponent. Guidance is provided on importance sampling densities that minimize variance.
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