Discrepancy Theory and Quasi-Monte Carlo Integration
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- 作者：Josef Dick (16)
Friedrich Pillichshammer (17) - 刊名：Lecture Notes in Mathematics
- 出版年：2014
- 出版时间：2014
- 年：2014
- 卷：2107
- 期：1
- 页码：539-619
- 全文大小：987 KB
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Friedrich Pillichshammer (17)
16. School of Mathematics and Statistics, The University of New South Wales, Sydney, NSW, 2052, Australia
17. Institute for Financial Mathematics, University of Linz, Altenbergerstra脽e 69, 4040, Linz, Austria - ISSN：1617-9692
文摘
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.