1998 Fiscal Year Final Research Report Summary
Random number theory and real analytic probability
| Project/Area Number |
09640268
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | KOBE UNIVERSITY |
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Principal Investigator |
FUKUYAMA Katusi Kobe University Faculty of Science Associate Professor, 理学部, 助教授 (60218956)
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| Co-Investigator(Kenkyū-buntansha) |
TAKAYAMA Nobuki Kobe University Faculty of Science Professor, 理学部, 教授 (30188099)
IKEDA Hiroshi Kobe University Faculty of Science Professor, 理学部, 教授 (10031353)
YAMAZAKI Tadashi Kobe University Faculty of Science Professor, 理学部, 教授 (30011696)
HIGUCHI Yasunari Kobe University Faculty of Science Professor, 理学部, 教授 (60112075)
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| Project Period (FY) |
1997 – 1998
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| Keywords | Central limit theorem / Monte Carlo method / quasi Monte Carlo method / uniformly distributed sequence / random numbers / M sequence / Hausdorff dimension / numerical integration |
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| Research Abstract |
Before our project, it had been proved that dependence of almost all irrational rotation vanish when it applied for the central limit theorem of Rademacher functions. This result explains why the quasi Monte Carlo methods are not effective in high dimensional space comparing with the ordinary Monte Carlo method.
Concerning this result, we classified irrational rotations and studied in detail on irrational rotations which generate the sequence converges to dependent stationary sequence. We have given conditions to have independent limit sequence and succeeded to have the numerically effective mean to verify the independence of limit.
We prove the central limit theorem for multiple n-ary transforms. This results is closely related to the theory of accelation of generation of random numbers by means of multiple transforms.
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