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Monte Carlo and Quasi-Monte Carlo Methods 2010 pp 23–41Cite as

Upper Bounds in Discrepancy Theory

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Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 23))

Abstract

Through the use of a few examples, we shall illustrate the use of probability theory, or otherwise, in the study of upper bound questions in the theory of irregularities of point distribution. Such uses may be Monte Carlo in nature but the most efficient ones appear to be quasi Monte Carlo in nature. Furthermore, we shall compare the relative merits of probabilistic and non-probabilistic techniques, as well as try to understand the actual role that the probability theory plays in some of these arguments.

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Author information

Authors and Affiliations

  1. Macquarie University, Sydney, NSW, 2109, Australia

    William W. L. Chen

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  1. William W. L. Chen
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Correspondence to William W. L. Chen .

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Editors and Affiliations

  1. , Institute of Applied Mathematics, University of Warsaw, Banacha 2, Warsaw, 02-097, Poland

    Leszek Plaskota

  2. , Institute of Applied Mathematics, University of Warsaw, Banacha 2, Warsaw, 02-097, Poland

    Henryk Woźniakowski

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Chen, W.W.L. (2012). Upper Bounds in Discrepancy Theory. In: Plaskota, L., Woźniakowski, H. (eds) Monte Carlo and Quasi-Monte Carlo Methods 2010. Springer Proceedings in Mathematics & Statistics, vol 23. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27440-4_2

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