Project/Area Number  03452011 
Research Category 
GrantinAid for Scientific Research (B).

Research Field 
General mathematics (including Probability theory/Statistical mathematics)

Research Institution  Hokkaido University 
Principal Investigator 
OKABE Yasunori Hokkaido University, Faculty of Science Professor, 理学部, 教授 (30028211)

CoInvestigator(Kenkyūbuntansha) 
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)
越 昭三 北海道大学, 理学部, 教授 (40032792)

Project Fiscal Year 
1991 – 1992

Project Status 
Completed(Fiscal Year 1992)

Budget Amount *help 
¥1,400,000 (Direct Cost : ¥1,400,000)
Fiscal Year 1992 : ¥1,400,000 (Direct Cost : ¥1,400,000)

Keywords  The theory of KMOLangevin equations / The theory of KM_2OLangevin equations / FluctuationDissipationTheorem / AlderWainwright effect / FluctuationDissipationPrinciple / Nonlinear prediction problem / Stationary Test / Causality Test / KM_2Oランジュヴァン方程式論 / 揺動散逸定理 / 非線形予測問題 / 定常性の検定 / 因果性の検定 / KM_2Oーランジュヴァン方程式 / 定常性 / 因果律 / 非線型予測問題 / KMOーランジュヴァン方程式 / 揺動散逸原理 
Research Abstract 
By developing the theory of KMOLangevin equations describing the time evolution of onedimensional weakly stationary processes with reflection positivity, we have obtained not only a unified mathematical embodiment of the fluctuationdissipationtheorem, but also elucidated the mathematical structure of AlderWainwright effect. In the course of the project above, we have grasped a philosophythe fluctuation dissipationprincipleas a guiding principle for the attitude of research in applying pure mathematics to applied science. Further, we have developed the theory of KM_2OLangevin equations for the multidimensional weakly stationary time series. We have applied the theory of KM_2OLangevin equations to be able to resolve the nonlinear prediction problem for the onedimensional strictly stationary time series , by obtaining a computable algorithm for the nonlinear 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.
