Consistency of randomized integration methods

03/31/2022

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by   Julian Hofstadler, et al.

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For integrable functions we provide a weak law of large numbers for structured Monte Carlo methods, such as estimators based on randomized digital nets, Latin hypercube sampling, randomized Frolov point sets as well as Cranley-Patterson rotations. Moreover, we suggest median modified methods and show that for integrands in L^p with p>1 a strong law of large numbers holds.