Discrepancy Theory and Quasi-Monte Carlo Integration

Chapter
First Online:
Part of the Lecture Notes in Mathematics book series (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.

Keywords

Monte Carlo Reproduce Kernel Hilbert Space Integration Error Lattice Rule Walsh Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Notes

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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© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsThe University of New South WalesSydneyAustralia
  2. 2.Institute for Financial MathematicsUniversity of LinzLinzAustria

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