Sparse-grid Gauss-Hermite quadrature is provably suboptimal at N^{-alpha/2}, while some QMC methods with change of variables achieve the optimal N^{-alpha} (ln N)^{(d-1)/2} rate in Gaussian Sobolev spaces.
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Optimality of quasi-Monte Carlo methods and suboptimality of the sparse-grid Gauss--Hermite rule in Gaussian Sobolev spaces
Sparse-grid Gauss-Hermite quadrature is provably suboptimal at N^{-alpha/2}, while some QMC methods with change of variables achieve the optimal N^{-alpha} (ln N)^{(d-1)/2} rate in Gaussian Sobolev spaces.