| Project/Area Number |
14340030
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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 | The University of Tokyo |
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Principal Investigator |
OKABE Yasunori The University of Tokyo, Graduate School of Engineering, Professor, 大学院・情報理工学系研究科, 教授 (30028211)
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| Co-Investigator(Kenkyū-buntansha) |
YANAGAWA Takashi Kurume University, Graduate School of Science, Professor, バイオ統計センター, 教授 (80029488)
MUROTA Kazuo The University of Tokyo, Graduate School of Engineering, Professor, 大学院・情報理工学系研究科, 教授 (50134466)
INOUE Akihiko Hokkaido University, Graduate School of Science, Associate Professor, 大学院・理学研究科, 助教授 (50168431)
HORITA Takehiko The University of Tokyo, Graduate School of Engineering, Professor, 大学院・情報理工学系研究科, 助教授 (90222281)
MATSUURA Masaya The University of Tokyo, Graduate School of Engineering, Assistant Professor, 大学院・情報理工学系研究科, 助手 (70334258)
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| Project Period (FY) |
2002 – 2004
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| Project Status |
Completed (Fiscal Year 2004)
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| Budget Amount *help |
¥9,100,000 (Direct Cost: ¥9,100,000)
Fiscal Year 2004: ¥2,400,000 (Direct Cost: ¥2,400,000)
Fiscal Year 2003: ¥2,300,000 (Direct Cost: ¥2,300,000)
Fiscal Year 2002: ¥4,400,000 (Direct Cost: ¥4,400,000)
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| Keywords | the theory of KM_2O-Langevin equations / non-linear filtering problem / test for stationarity / test for abnormality / separation property / earthquake / aurora / brain wave / KM_2O-ランジュヴン方程式 / 揺動散逸定理 / 定常解析 / 異常解析 / 決定解析 / 深部低周波地震 / 大脳皮質脳波 / KM_2O-ランジュヴァン方程式 / 非線形情報解析 / 非線形フィルタリング問題 / 定常性テスト Test(S) / 異常性テスト(ABN) / KM_2O-Langevin equations / non-linear information analysis / generating system / non-arbitrage pricing for option / stationarity test / abnormality test / fluctuation-dissipation theorem / from data to model |
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| Research Abstract |
We have obtained a formula for calculating a nonlinear filter between two discrete time stochastic processes, by using the theory of KM_2O-Langevin equations. Then we have applied it to a concrete non-linear system consisting of signal process and observation process, and given a solution for the non-linear filtering problem by obtaing an algorithm for calculating the non-linear fiter, which had been unsolved since Kalman-Bucy's work.
By definning the abnormality of time series as the degree of breakdown of stationarity of time series, we have proposed Test(ABN) for catching certain signs of the abnormality of time series, by using Test(S) for testing the stationarity of time series and the generating system of polynomial type for the nonlinear information spaces associated with the discrete time stochastic processes.
By applying Test(ABN) and Test(D) for testing the determinacy of time series to the time series of earthquakes, aurora and brain waves, we have discovered a new qualitative property, to be called separation property, on the region possessing stationarity after the arrival of S-wave for the deep low frequency earthquakes, the occurrence of aurora, and on the total region possessing stationarity of ECoG. This separation property do not appear for the usual earthquakes and EEG.
By treating the continuous time stationary process X whose gloval time evolution is governed by [α, β, γ]-Langevin equation, we have derived both the continuous time KM_2O-Langevin equation describing the local time evolution the stochastic process X and the system of equations characterizing the coefficients appearing in the above equation.
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