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arXiv · 1406.0230

Functions of bounded variation, signed measures, and a general Koksma-Hlawka inequality

Christoph Aistleitner·Josef Dick
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Abstract

In this paper we prove a correspondence principle between multivariate functions of bounded variation in the sense of Hardy and Krause and signed measures of finite total variation, which allows us to obtain a simple proof of a generalized Koksma--Hlawka inequality for non-uniform measures. Applications of this inequality to importance sampling in Quasi-Monte Carlo integration and tractability theory are given. Furthermore, we discuss the problem of transforming a low-discrepancy sequence with respect to the uniform measure into a sequence with low discrepancy with respect to a general measure $\mu$, and show the limitations of a method suggested by Chelson.

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Christoph Aistleitner, Josef Dick. 2014-06-02. Functions of bounded variation, signed measures, and a general Koksma-Hlawka inequality. https://arxiv.org/abs/1406.0230

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