擬似乱数と超一様分布列 : 最近の話題(<小特集>モンテカルロシミュレーション)

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This paper overviews two recent topics on pseudorandom numbers and low-discrepancy sequences. The first topic is on the Mersenne Twister random number generator. We show that while Mersenne Twister is almost the best in terms of the generation efficiency, it has a defect in terms of equidistribution property in high dimensions. The importance of improving the "quality" of Mersenne Twister is explained. The second topic is on GFaure (generalized Faure) sequences. We describe the construction method of GFaure sequences as well as recent theoretical results on the efficiency of GFaure sequences particularly for the high-dimensional integration problems associated with financial engineering. Finally, we mention an open question related to financial applications of low-discrepancy sequences.
2003-12-15