| Project/Area Number |
13640145
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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 | Okayama University of Science |
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Principal Investigator |
TAKENAKA Shigeo Okayama University of Science, Dept. of Science, Professor, 理学部, 教授 (80022680)
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| Co-Investigator(Kenkyū-buntansha) |
KOJO Katsuya Niihama College of Technology, Mathematics and Science, Lecturer, 理数科, 講師 (10280471)
TAKASHIMA Keizo Okayama University of Science, Dept. of Science, Professor, 理学部, 教授 (00137184)
渡辺 寿夫 岡山理科大学, 理学部, 教授 (40037677)
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| Project Period (FY) |
2001 – 2002
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| Project Status |
Completed (Fiscal Year 2002)
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| Budget Amount *help |
¥1,100,000 (Direct Cost: ¥1,100,000)
Fiscal Year 2002: ¥1,100,000 (Direct Cost: ¥1,100,000)
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| Keywords | stable random fields / random processes / determinsim / multi-dimensional time / 決定性 / stable process / set Indexed fields / determinism |
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| Research Abstract |
Random fields with parameter in subsets of a certain measure space are called Set-Indexed Random Fields and have a special property called determinism. A Gaussian system has 2-dimensional determinism, that is, the higher dimensional distributions of the system are completely determined by their own 1-dimensional and 2-dimensional (covariances) marginal distributions. On the contrary, there are some examples of non-Gaussian set-indexed random fields which are determined by their 3-dimensional marginals but not determined by 2-dimensional marginals.
Let fix a convex cone V in the n-dimensional Euclidean space. A curve L is called time-like if for any point x in L, the "future" of the line is included in V+x, and the "past" is included in -V+x. An n-parameter random field X is called multi-parameter additive process if the restriction X|L on any time-like curve L is an additive process, that is X|L has independent and uniform increments. In this research, we obtained a characterization of n-parameter additie processes as set-indexed processes.
Also, a characterization of 1-parameter processes valued in the space of time-like curves is obtained.
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