1998 Fiscal Year Final Research Report Summary
Study of infinite dimensional stochastic analysis and stochastic numerical analysis
| Project/Area Number |
09440084
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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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 | KYUSHU UNIVERSITY |
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Principal Investigator |
SUGITA Hiroshi Kyushu Univ., Graduate School of Math, Asso.Prof., 大学院・数理学研究科, 助教授 (50192125)
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| Co-Investigator(Kenkyū-buntansha) |
OGAWA Shigeyoshi Kanazawa Univ., Faculty of Engineering, Professor, 工学部, 教授 (80101137)
KUWAE Kazuhiro Saga Univ., Faculty of Science and Engineering, Asso.Prof., 理工学部, 助教授 (80243814)
OGURA Yukio Saga, Univ., Faculty of Science and Engneering, Professor, 理工学部, 教授 (00037847)
TANIGUCHI Setsuo Kyushu Univ., Graduate School of Math., Asso.Prof., 大学院・数理学研究科, 助教授 (70155208)
KUNITA Hiroshi Kyushu Univ., Graduate School of Math., Professor, 大学院・数理学研究科, 教授 (30022552)
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| Project Period (FY) |
1997 – 1998
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| Keywords | Weyl transformation / numerical integration / Monte-Carlo method / Wiener space / multiple Wiener Integral / Oscillatory integral / Malliavin calculus |
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| Research Abstract |
Results in infinite dimensional stochastic analysis
SUGITA and TANIGUCHI investigated the oscillatory integrals on an abstract Wiener space and got the following result Let the phase function be a double Wiener integral and let the amplitude function be a multiple Wiener integral. If it is impossible to define properly the value of the amplitude function at the origin, the behavior of the oscillatory integral becomes quite different from finite dimensional cases.
SUGITA and TAKANOBU got the following result Let {f^<(m)>}_m be a sequence of symmetric statistics of m variables. Then the sequence of random variables {f^<(m)>(chi+nalpha)}_n on the *-dimensional torus converges as m * * to the i.i.d. of multile Wiener intgerals.
Results in stochastic numerical analysis
From Jan.27 to Jan.30, we held a reseach conference "Probability theorey and computational mathematics" at Kyushu University. SUGITA gave a talk there with title "Pseudorandom number generation by means of irrational rotation-Fourier series approach". From Nov.9 to Nov.11, we held a research conference "The theory and methods of stochastic numerical analysis" at Kanazawa university. SUGITA gave a talk there with title "Robustness of quasi-Monte Carlo methods".
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