×

zbMATH — the first resource for mathematics

Comparison of methods for the simulation of a Gaussian white noise. (Comparaison des méthodes de simulation d’un bruit blanc gaussien.) (French) Zbl 0972.65501
Summary: We present a theoretical and practical study of the autocovariance function of a Gaussian white noise simulated by the inversion method, the Box-Muller method and normal approximation. We show that the inversion method does not generate a Gaussian process and that the normal approximation is the most efficient.
MSC:
65C99 Probabilistic methods, stochastic differential equations
PDF BibTeX XML Cite
Full Text: Numdam EuDML
References:
[1] Bailey , B.J.R. ( 1981 ) : Alternatives to Hastings’approximation to the inverse of the normal cumulative distribution function . Appl.Statist. , 30 , N^\circ . 3 , pp. 275 - 276 . MR 642779
[2] Bosq , D. et Lecoutre , J. P ( 1987 ) : théorie de l’estimation fonctionnelle . Ed Economica . · Zbl 0236.62024
[3] Box , J.E.P. and Muller , M.E. ( 1958 ) : A note on the generation of random normal deviates . Ann.Math. Statist. , 29 , pp. 610 - 611 . Article | Zbl 0085.13720 · Zbl 0085.13720 · doi:10.1214/aoms/1177706645 · minidml.mathdoc.fr
[4] Golder , E.R. and Setle , J.G. ( 1976 ) : The Box-Muller method for generating pseudo-random normal deviates . Appl. Statist. , 25 , N^\circ . 1 , pp. 12 - 20 . MR 428682
[5] Hastings , C. ( 1955 ) : Approximation for digital computers . Princeton University Press . MR 68915 | Zbl 0066.10704 · Zbl 0066.10704
[6] Hugo , C.H. ( 1978 ) : Approximating the cumulative normal distribution and its inverse . Appl. Statist. , 27 , N^\circ . 1 ., pp. 76 - 77 .
[7] Lehmer , D.H. ( 1951 ) : Mathematical methods in large scale digital computing units. Proceedings of second symposium on large scale digital calculating machinery . Ann. Comput. Lab. Harvard University , V. 26 , pp. 141 - 146 . MR 44899 | Zbl 0045.40001 · Zbl 0045.40001
[8] Neave , H.R. ( 1973 ) : On using the Box-Muller transformation with multiplicative congruential pseudo-random number generators . Appl. Statist. , 22 , pp. 92 - 97 .
[9] Page , E. ( 1978 ) : Approximation to the cumulative normal function and its inverse for use on a pocket calculator . Appl. Statist. , V. 26 , N^\circ . 1 , pp. 75 - 76 .
[10] Smili , D. ( 1990 ) : Contribution à l’étude probabiliste des générateurs d’échantillons de séries temporelles . Thèse de l’ Université Paris 6.
[11] Zelen , M. and Severo , N.C. ( 1966 ) : Probability functions . In handbook of mathematical functions (M. Abramowitz and I. A. Stegun, eds). Washington. D.C . : Department of commerce of U.S. Government .
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.