An improvement of Koksma's inequality and convergence rates for the quasi-Monte Carlo method

02/08/2020

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by   Martin Lind, et al.

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When applying the quasi-Monte Carlo (QMC) method of numerical integration, Koksma's inequality provides a basic estimate of the error in terms of the discrepancy of the used evaluation points and the total variation of the integrated function. We present an improvement of Koksma's inequality that is also applicable for functions with infinite total variation. As a consequence, we derive error estimates for the QMC integration of functions of bounded p-variation.