On the use of low discrepancy sequences in Monte Carlo methods

Monte Carlo Methods and Applications

Volumn 2, Issue 4, 1996, Pages 295-320

  Tuffin, Bruno ^a  

^a CAMPUS DE BEAULIEU   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000501691     PISSN: 09299629     EISSN: 15693961     Source Type: Journal    
DOI: 10.1515/mcma.1996.2.4.295     Document Type: Article

References (29)

1. I.A. Antonov and Saleev V.M. An economic method of computing/pr- sequences. USSR Computational Math, and Math. Phys., 19(1979), 1, 252-256.
2. J. Beck and W. Chen. Irregularities of Distribution. Cambridge University Press, 1987.
3. J.P. Borel, G. Pages, and Y. Xiao. Probabilites numeriques, chapter suites a discrepance faible et integration numerique. INRIA, 1991. collection didactique.
4. N. Bouleau and D. Lepingle. Numerical methods for stochastic processes. John Wiley and Sons, 1993.
5. E. Braaten and G. Weller. An Improved Low-Discrepancy Sequence for Multidimensional Quasi-Monte Carlo Integration. J. Comput. Phys., 33(1979), 249-258.
6. R. Cranley and T.N.L. Patterson. Randomization of number theoretic methods for multiple integration. SIAM J. Numer. Anal., 13(1976), 6, 904-914.
7. H. Faure. Discrepances de suites associees a un Systeme de numeration (en dimension un). Bull. Soc. Math. France, 109(1981), 143-182.
8. H. Faure. Discrepances de suites associees a un Systeme de numeration (en dimension s). Acta Arith., 41(1982), 337-351.
9. H. Faure. Good Permutations for Extreme Discrepancy. Journal of Number Theory, 42(1992), 47-56.
10. B. L. Fox. Algorithm 647:Implementation and Relative Efficiency of Quasirandom Sequence Generators. ACM Transactions on Mathematical Software, 12(1986), 4,362-376.
11. B. L. Fox. Algorithm 659: Implementing Sobol's Quasirandom Sequence Generator. ACM Transactions on Mathematical Software, 14(1988), 1, 88-100.
12. B. L. Fox, P. Bratley, and H. Niederreiter. Implementation and test of low discrepancy sequences. ACM Trans. Model. Comput. Simui, 2(1992), 3, 195-213.
13. J. M. Hammersley and D. C. Handscomb. Monte Carlo Methods. Methuen, London, 1964.
14. L. K. Hua and Y. Wang. Applications of Number Theory to Numerical Analysis. Springer Verlag, 1981.
15. H. Kalos and A. Whitlock. Monte Carlo Methods, vol. 1: Basics. John Wiley, New York, 1986.
16. H. Niederreiter. Quasi-Monte Carlo Methods and Pseudo-Random Numbers. Bulletin of the American Mathematical Society, 84(1978), 957-1041.
17. H. Niederreiter. Random Number Generation and Quasi-Monte Carlo Methods. CBSM 63, 1992.
18. A. B. Owen. Monte Carlo Variance of Scrambled Equidistribution Quadrature. Technical report, Department of Statistics, Stanford University, 1994.
19. A. B. Owen. Randomly permuted (t, m, s)-nets and (*, s)-sequences. In Harald Niederreiter and Peter Jau-Shyong Shiue, editors, Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing, volume 106 of Lecture Notes in Statistics, pages 299-315. Springer, 1995.
20. G. Pages and Y.J. Xiao. Sequences with low discrepancy and pseudo-random numbers: theoretical results and numerical tests, to appear in J. Statist. Comput. Simulat., 1996.
21. W.H. Press, S.A. Teutolsky, W.T. Vetterling, and B.P. Flannery. Numerical recipes in C: the art of scientific computing. Cambridge; New York; Oakeigh: Cambridge university press, 1992.
22. P. K. Sarkar and M. A. Prasad. A Comparative Study of Pseudo and Quasi Random Sequences for the Solution of Integral Equations. Journal of Computational Physics, 68(1987), 66-88.
23. J. E. H. Shaw. A quasirandom approach to integration in Bayesian statistics. Ann. Statist, 16(1988), 895-914.
24. I.M. Sobol. The distribution of points in a cube and the approsimate evaluation of integrals. USSR Computational Math, and Math. Phys., 7(1967), 86-112.
25. I.M. Sobol'. Uniformly distributed sequences with an additional uniform property. USSR Computational Math, and Math. Phys., 16(1976), 5, 236-242.
26. B. Tuffin. Improvement of Halton sequences distribution. Technical Report 998, IRISA, March 1996.
27. B. Tuffin. Variance reduction technique for a cellular system with dynamic resource sharing. In Proceedings of the 10th European Simulation Multiconference, pages 467-471, Budapest, June 1996.
28. B. Tuffin. Variance Reductions applied to Product-Form Multi-Class Queuing Network: antithetic variates and low discrepancy sequences. Technical Report 1005, IRISA, April 1996.
29. S. K. Zaremba. Some applications of multidimensionnal integration by parts. Ann. Pol. Math, XXI(1968), 85-96.