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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
H. Faure, Discrépance de suites associées à un système de numération (en dimension 1), Bull. Soc. math. France 109 (1981), 143–182.
H. Faure, Using Permutations to Reduce Discrepancy, Journal of Computational and Applied Mathematics 31 (1990), 97–103.
H. Faure, Good Permutations for Extreme Discrepancy, Journal of Number Theory 41 (1992), 47–56.
H. Faure, Variations on (0,s)-sequences, Journal of Complexity, to appear.
F.J. Hickernell, The Mean Square Discrepancy of Randomized Nets, ACM Trans. Model.Comput.Simul. 6 (1996), 274–296.
J. Matousek, On the L 2-discrepancy for Anchored boxes, Journal of Complexity 14 (1998), 527–556.
J. Matousek, Geometric Discrepancy: An Illustrated Guide, Springer, 1999.
H. Niederreiter, Point Sets and Sequences with Small Discrepancy, Monatsh. Math. 104 (1987), 273–337.
H. Niederreiter, Random Number Generation and Quasi-Monte Carlo Methods, CBMS-NSF Regional Conference Series in Applied Mathematics 63, SIAM, 1992.
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.
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.
S. Tezuka, Polynomial Arithmetic Analogue of Halton Sequences, ACM Tomacs 3-2 (1993), 99-107.
S. Tezuka, A Generalization of Faure Sequences and its Efficient Implementation, Research Report IBM RT0105 (1994), 1–10.
S. Tezuka, Uniform Random Numbers: Theory and Practice, Kluwer Academic Publishers, Boston, 1995.
S. Tezuka, Quasi-Monte Carlo — Discrepancy between Theory and Practice, mcqmc2000, Springer-Verlag, in this volume.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
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
Download citation
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
eBook Packages: Springer Book Archive