A strong law of large numbers for scrambled net integration

@article{Owen2020ASL,
  title={A strong law of large numbers for scrambled net integration},
  author={Art B. Owen},
  journal={SIAM Rev.},
  year={2020},
  volume={63},
  pages={360-372}
}
  • A. Owen
  • Published 18 February 2020
  • Mathematics
  • SIAM Rev.
This article provides a strong law of large numbers for integration on digital nets randomized by a nested uniform scramble. The motivating problem is optimization over some variables of an integral over others, arising in Bayesian optimization. This strong law requires that the integrand have a finite moment of order $p$ for some $p>1$. Previously known results implied a strong law only for Riemann integrable functions. Previous general weak laws of large numbers for scrambled nets require a… 
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