Dynamic random Weyl sampling for drastic reduction of randomness in Monte Carlo integration

Authors:
Hiroshi Sugita
Affiliations:
Faculty of Mathematics, Graduate School of Mathematics, Kyushu University, 6-10-1 Hakozaki, Higashi-ku, 812-8581 Fukuoka, Japan
Venue:
Mathematics and Computers in Simulation - Special issue: 3rd IMACS seminar on Monte Carlo methods - MCM 2001
Year:
2003

Citing 2
Cited 1

Pseudorandomness and Cryptographic Applications

Pseudorandomness and Cryptographic Applications
Robust numerical integration and pairwise independent random variables

Journal of Computational and Applied Mathematics

Monte-Carlo Integration Using Cryptographically Secure Pseudo-random Generator

NMA '02 Revised Papers from the 5th International Conference on Numerical Methods and Applications

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Abstract

To reduce randomness drastically in Monte Carlo (MC) integration, we propose a pairwise independent sampling, the dynamic random Weyl sampling (DRWS). DRWS is applicable even if the length of random bits to generate a sample may vary. The algorithm of DRWS is so simple that it works very fast, even though the pseudo-random generator, the source of randomness, might be slow. In particular, we can use a cryptographically secure pseudo-random generator for DRWS to obtain the most reliable numerical integration method for complicated functions.