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A Panorama of Discrepancy Theory pp 539–619Cite as

Discrepancy Theory and Quasi-Monte Carlo Integration

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Part of the book series: Lecture Notes in Mathematics ((LNM,volume 2107))

Abstract

In this chapter we show the deep connections between discrepancy theory on the one hand and quasi-Monte Carlo integration on the other. Discrepancy theory was established as an area of research going back to the seminal paper by Weyl [117], whereas Monte Carlo (and later quasi-Monte Carlo) was invented in the 1940s by John von Neumann and Stanislaw Ulam to solve practical problems. The connection between these areas is well understood and will be presented here. We further include state of the art methods for quasi-Monte Carlo integration.

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Acknowledgements

The first author is supported by a Queen Elizabeth II Fellowship from the Australian Research Council. The second author is partially supported by the Austrian Science Foundation (FWF), Project S9609, that is part of the Austrian National Research Network “Analytic Combinatorics and Probabilistic Number Theory” and Project F5509-N26, that is part of the Special Research Program “Quasi-Monte Carlo Methodes: Theory and Applications”.

The authors thank Michaela Szölgyenyi and Henryk Woźniakowski for many helpful suggestions.

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  1. School of Mathematics and Statistics, The University of New South Wales, Sydney, NSW, 2052, Australia

    Josef Dick

  2. Institute for Financial Mathematics, University of Linz, Altenbergerstraße 69, 4040, Linz, Austria

    Friedrich Pillichshammer

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  1. Josef Dick
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  2. Friedrich Pillichshammer
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Correspondence to Josef Dick .

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  1. Department of Mathematics, Macquarie University, Sydney, New South Wales, Australia

    William Chen

  2. Department of Computer Science, Kiel University, Kiel, Germany

    Anand Srivastav

  3. Dipartimento di Statistica e Metodi Quantitativi, Università di Milano-Bicocca, Milano, Italy

    Giancarlo Travaglini

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Dick, J., Pillichshammer, F. (2014). Discrepancy Theory and Quasi-Monte Carlo Integration. In: Chen, W., Srivastav, A., Travaglini, G. (eds) A Panorama of Discrepancy Theory. Lecture Notes in Mathematics, vol 2107. Springer, Cham. https://doi.org/10.1007/978-3-319-04696-9_9

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