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Another Random Scrambling of Digital (t,s)-Sequences

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Monte Carlo and Quasi-Monte Carlo Methods 2000

Abstract

This paper presents a new random scrambling of digital (t,s)-sequences and its application to two problems from finance, showing the usefulness of this new class of randomized low-discrepancy sequences; moreover the simplicity of the construction allows efficient implementation and should facilitate the derandomization in this particular class; also the search of the effective dimension in high dimensional applications should be improved by the use of such scramblings.

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References

  1. H. Faure, Discrépance de suites associées à un système de numération (en dimension 1), Bull. Soc. math. France 109 (1981), 143–182.

    MathSciNet  MATH  Google Scholar 

  2. H. Faure, Using Permutations to Reduce Discrepancy, Journal of Computational and Applied Mathematics 31 (1990), 97–103.

    Article  MathSciNet  MATH  Google Scholar 

  3. H. Faure, Good Permutations for Extreme Discrepancy, Journal of Number Theory 41 (1992), 47–56.

    Article  MathSciNet  Google Scholar 

  4. H. Faure, Variations on (0,s)-sequences, Journal of Complexity, to appear.

    Google Scholar 

  5. F.J. Hickernell, The Mean Square Discrepancy of Randomized Nets, ACM Trans. Model.Comput.Simul. 6 (1996), 274–296.

    Article  MathSciNet  MATH  Google Scholar 

  6. J. Matousek, On the L 2-discrepancy for Anchored boxes, Journal of Complexity 14 (1998), 527–556.

    Article  MathSciNet  MATH  Google Scholar 

  7. J. Matousek, Geometric Discrepancy: An Illustrated Guide, Springer, 1999.

    Google Scholar 

  8. H. Niederreiter, Point Sets and Sequences with Small Discrepancy, Monatsh. Math. 104 (1987), 273–337.

    Article  MathSciNet  MATH  Google Scholar 

  9. H. Niederreiter, Random Number Generation and Quasi-Monte Carlo Methods, CBMS-NSF Regional Conference Series in Applied Mathematics 63, SIAM, 1992.

    Google Scholar 

  10. H. Niederreiter and C.P. Xing, Nets, (t,s)-sequences and Algebraic Geometry, in Lecture Notes in Statistics 138 (P. Hellekalek and G.% Larcher, Ed.) Springer (1998), 267–302.

    Google Scholar 

  11. A. Owen, Randomly Permuted (t,m,s)-nets and (t,s)-sequences, in Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing (H. Niederreiter and P. Shiue, Ed.) Springer-Verlag (1995), 299–317.

    Google Scholar 

  12. S. Tezuka, Polynomial Arithmetic Analogue of Halton Sequences, ACM Tomacs 3-2 (1993), 99-107.

    Google Scholar 

  13. S. Tezuka, A Generalization of Faure Sequences and its Efficient Implementation, Research Report IBM RT0105 (1994), 1–10.

    Google Scholar 

  14. S. Tezuka, Uniform Random Numbers: Theory and Practice, Kluwer Academic Publishers, Boston, 1995.

    Book  MATH  Google Scholar 

  15. S. Tezuka, Quasi-Monte Carlo — Discrepancy between Theory and Practice, mcqmc2000, Springer-Verlag, in this volume.

    Google Scholar 

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Faure, H., Tezuka, S. (2002). Another Random Scrambling of Digital (t,s)-Sequences. In: Fang, KT., Niederreiter, H., Hickernell, F.J. (eds) Monte Carlo and Quasi-Monte Carlo Methods 2000. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-56046-0_16

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  • DOI: https://doi.org/10.1007/978-3-642-56046-0_16

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42718-6

  • Online ISBN: 978-3-642-56046-0

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