1986 Fiscal Year Final Research Report Summary
Representation of stochastic processes and the limit theorem.
| Project/Area Number |
60540141
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| Research Category |
Grant-in-Aid for General Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Faculty of Science, Kumamoto University |
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Principal Investigator |
HITSUDA Masuyuki Faculty of Science, Kumamoto University, 理学部, 教授 (50024237)
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| Co-Investigator(Kenkyū-buntansha) |
OKA Yukimasa Faculty of Science, Kumamoto University, 理学部, 助教授 (50089140)
OSHIMA Yoichi Faculty of Engineering, Kumamoto University, 工学部, 教授 (20040404)
KOHNO Mitsuhiko Faculty of Science, Kumamoto University, 理学部, 教授 (30027370)
TAKADA Yoshikazu Faculty of Science, Kumamoto University, 理学部, 講師 (70114098)
YOSHIDA Kiyoshi Faculty of Science, Kumamoto University, 理学部, 助教授 (80033893)
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| Project Period (FY) |
1985 – 1986
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| Keywords | Gaussian processes / canonical representation / innovation / Bruwnian motoon / ホワイトノイズ |
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| Research Abstract |
Under the title "Representation of Stochastic processes and the limit theorem", we have well organized a research system on mathematical analysis, and we could obtain many results in wide fields. The main contents are (1) Representaion of Gaussian processes, (2) Mouvements of infinite particles and the limit theorem, (3) Analysis of Markov processes by means of Dirichlet forms, and(4) Data analysis in the field of probability theory, and moreover (5) Global analvsis of ordinary differentian equations and the numerical treatment, (6) Super-sub solutions of elliptic partial differential equations of non linear type, in the field of functional equations. The head investigator concerns representation theory of Gaussian processes and the limit behavior of infinitely many interacting particles. Some new sufficient conditions for a Gaussian process to have tha single innovations has been obtained.
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