1992 Fiscal Year Final Research Report Summary
A study of stationarity and causality based on the theory of KM_2O-Langevin equations
| Project/Area Number |
03452011
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| Research Category |
Grant-in-Aid for General Scientific Research (B)
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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 | Hokkaido University |
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Principal Investigator |
OKABE Yasunori Hokkaido University, Faculty of Science Professor, 理学部, 教授 (30028211)
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| Co-Investigator(Kenkyū-buntansha) |
INOUE Akihiko Hokkaido University, Faculty of Science Lecturer, 理学部, 講師 (50168431)
ARAI Asao Hokkaido University, Faculty of Science Associate Professor, 理学部, 助教授 (80134807)
NAKAZI Takahiko Hokkaido University, Faculty of Science Professor, 理学部, 教授 (30002174)
KISHIMOTO Akitaka Hokkaido University, Faculty of Science Professor, 理学部, 教授 (00128597)
AGEMI Rentaro Hokkaido University, Faculty of Science Professor, 理学部, 教授 (10000845)
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| Project Period (FY) |
1991 – 1992
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| Keywords | The theory of KMO-Langevin equations / The theory of KM_2O-Langevin equations / Fluctuation-Dissipation-Theorem / Alder-Wainwright effect / Fluctuation-Dissipation-Principle / Non-linear prediction problem / Stationary Test / Causality Test |
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| Research Abstract |
By developing the theory of KMO-Langevin equations describing the time evolution of one-dimensional weakly stationary processes with reflection positivity, we have obtained not only a unified mathematical embodiment of the fluctuation-dissipation-theorem, but also elucidated the mathematical structure of Alder-Wainwright effect.
In the course of the project above, we have grasped a philosophy-the fluctuation- dissipation-principle-as a guiding principle for the attitude of research in applying pure mathematics to applied science. Further, we have developed the theory of KM_2O-Langevin equations for the multi-dimensional weakly stationary time series. We have applied the theory of KM_2O-Langevin equations to be able to resolve the non-linear prediction problem for the one-dimensional strictly stationary time series , by obtaining a computable algorithm for the non-linear predictor, which is submitted to J. Math. Soc. Japan.
Moreover, as applications to data analysis, we are going to develop a new project which consisits of the four part: the stationary analysys, the causal analysys, the entropy analysys and the prediction analysis. A work concernig causal analysis is submitted to Nagoya Math. J.
Our next aim is to search certain dynamics behind complex system like chaotic system and then predict its future, by using the project above.
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