# 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} }

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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