1990 Fiscal Year Final Research Report Summary
Separation and Fusion of Information in Stochastic Processes.
| Project/Area Number |
01540190
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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 | Kumamoto University |
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Principal Investigator |
HITSUDA Masuyuki Kumamoto University Fac. Sci. Professor, 理学部, 教授 (50024237)
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| Co-Investigator(Kenkyū-buntansha) |
SAISHO Yasumasa Kumamoto University Fac. Eng., Lecturer., 工学部, 講師 (70195973)
OKA Yukimasa Kumamoto University Fac. Sci., Ass, Professor, 理学部, 助教授 (50089140)
OSHIMA Yoichi Kumamoto University Fac. Eng. Professor, 工学部, 教授 (20040404)
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| Project Period (FY) |
1989 – 1990
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| Keywords | Gaussian process / Brownian motion / Canonical representation / filtering / innovation / stochastic integral / stochastic equation. |
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| Research Abstract |
Stochastic processes, especially Gaussian processes, increase their own information as time-parameter is increasing. The fact is described in terms of the increasing systems of sigma-fields generated by the "past" of the processes. It is generally difficult to find out the structure of the increasing system of the sigma-fields. In the theory of Gaussian processes, the structures are considered by P. Levy, T. Hida and many authors. The so-called Levy-Hida canonical representation makes it possible to find out the innovation from a given Gaussian process. In other words, we can find how many independent increments processes are included in the Gaussian process. In the present investigation, a Gaussian semimartingale is considered from the view point of the "innovation problems". The main results are (1) establishment of necessary an d sufficient condition for a Gaussian semimartingale to have the single innovation (equivalently to have multiplicity one), and (2) an extension of the innovation theorem due to Shiryaev and Kailath. The second result is well applicable to the theory of canonical representation.
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