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Journal of Zhejiang University SCIENCE A 2002 Vol.3 No.3 P.339-343

http://doi.org/10.1631/jzus.2002.0339


B-splines smoothed rejection sampling method and its applications in quasi-Monte Carlo integration


Author(s):  LEI Gui-yuan

Affiliation(s):  Department of Mathematics, Zhejiang University, Hangzhou 310028, China

Corresponding email(s):   guiyuanlei@elong.com

Key Words:  Quasi-Monte Carlo, Monte Carlo, B-splines, Importance sampling, Numerical integration


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LEI Gui-yuan. B-splines smoothed rejection sampling method and its applications in quasi-Monte Carlo integration[J]. Journal of Zhejiang University Science A, 2002, 3(3): 339-343.

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Abstract: 
The rejection sampling method is one of the most popular methods used in monte Carlo methods. It turns out that the standard rejection method is closely related to the problem of monte Carlo%29&ck%5B%5D=abstract&ck%5B%5D=keyword'>quasi-monte Carlo integration of characteristic functions, whose accuracy may be lost due to the discontinuity of the characteristic functions. We proposed a b-splines smoothed rejection sampling method, which smoothed the characteristic function by b-splines smoothing technique without changing the integral quantity. Numerical experiments showed that the convergence rate of nearly O(N-1) is regained by using the b-splines smoothed rejection method in importance sampling.

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Reference

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[2] Fang, K.T., Wang, Y., 1994. Number-Theoretic Methods in Statistics. Chapman & Hall, London, p.12-14.

[3] Moskowitz, B., Caflisch R.E., 1996. Smoothness and dimension reduction in quasi-monte carlo methods. Math. Comput. Modelling. 23(8-9):37-54.

[4] Niederreiter, H., 1992. Random Number Generation and Quasi-Monte Carlo Methods. SIAM, Philadel, p. 1-241.

[5] Press, W.H., Teukolsky, S.A., Vetterling, W.T., Flannery, B.P.,1992. Numerical Recipes in C: The Art of Scientific Computing. Cambridge University Press(2nd ed.), New York, p. 278-283.

[6] Schumaker, L., 1981. Spline Functions: Basic Theory. Wiley, New York, p. 118-134.

[7] Wang Xiaoqun, 2000. Improving the rejection sampling method in quasi-Monte Carlo methods. Journal of computational and applied Mathematics. 114: 231-246.

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