2006 Fiscal Year Final Research Report Summary
Nonlinear analysis on Innovation of stochastic processes and random fields
| Project/Area Number |
17540128
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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 | Aichi Prefectural University |
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Principal Investigator |
SI Si Aichi Prefectural University, Faculty of Information Science and Technology, Associate Professor, 情報科学部, 助教授 (70269687)
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| Co-Investigator(Kenkyū-buntansha) |
SHIROMOTO Keisuke Aichi Prefectural University, Faculty of Information Science and Technology, Associate Professor, 情報科学部, 助教授 (00343666)
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| Project Period (FY) |
2005 – 2006
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| Keywords | Innovation / Stochastic processes / Stable distribution / Gauss distribution / White noise / Poisson noise / duality / generalized function |
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| Research Abstract |
The research result of this year involves three topics as are summarized below.
1) Innovation approach to stochastic processes.
To obtain innovation is one of the best ways to investigate evolutional random complex systems, so that the research of this problem started last year and has been carried over to this year. In the important cases, the innovation is the time derivative of an additive process. Innovation problem has therefore close connections with the Levy decomposition of an additive process. Thus, we have established the system of idealized elemental random variables as the innovation of the given random complex system.
2) Fractional power distributions.
It has been recognized that fractional power distributions appear in many fields of science and play important roles. For the study of this distribution, I have proposed to embed those distributions into an additive process, so that we can study the reason why such a fractional distribution arises. There are many cases where embedding into a stable process is possible. In those cases, the Levy decomposition of the stable process can be applied and the results tell us hidden statistical properties of the phenomena with fractional power distribution.
3) Duality between Gaussian and Poisson noises.
Gaussian white noise and Poisson noise can be dealt with in a similar manner on the one hand, but dissimilarity is significant on the other. One of the realizations of dissimilarity can be seen in the duality between the two noises. In connection with the infinite symmetric group, I have given a duality of the two noises.
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Research Products
(16 results)
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[Journal Article] ポアソンのイズの話題2006
Author(s)
Si Si
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Journal Title
Proceeding of Symposium on History of Mathematics, Research center of Computational Math. Science, Tsudajuku University, 27
Pages: 216-228
Description
「研究成果報告書概要(和文)」より
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[Journal Article] A topic on Poisson noise2006
Author(s)
Si Si
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Journal Title
Proceeding of Symposium on History of Mathematics, Research center of Computational Math. Science, Tsudajuku University 27
Pages: 216-228
Description
「研究成果報告書概要(欧文)」より
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