CoInvestigator(Kenkyūbuntansha) 
NAKANO Yuji Department of Economy, Shiga University, Professor, 経済学部, 教授 (60024981)
OKANO Takaaki Joint Stock of Nihon UNISYS, Head (reseach position), 応用ソフトウエア部, 部長(研究職)
YANAGAWA Takashi Graduate School of Science, Kyushu University, Professor, 大学院・数理学研究院, 教授 (80029488)
HORITA Takehiko Graduate School of Engineering, Lecturer, 大学院・工学系研究科, 講師 (90222281)
AIHARA Kazuyuki Graduate School of Frontier Sciences, University of Tokyo Professor, 大学院・新領域創成科学研究科, 教授 (40167218)
伏見 正則 東京大学, 大学院・工学系研究科, 教授 (70008639)

Budget Amount *help 
¥12,700,000 (Direct Cost: ¥12,700,000)
Fiscal Year 2000: ¥3,200,000 (Direct Cost: ¥3,200,000)
Fiscal Year 1999: ¥2,700,000 (Direct Cost: ¥2,700,000)
Fiscal Year 1998: ¥6,800,000 (Direct Cost: ¥6,800,000)

Research Abstract 
We constructed a theory of KM_2OLangevin equations for flows in a vector space with a metric in which a characterization theorem that characterizes stationarity of flow in terms of the fluctuationdissipation theorem, a construction theorem of stationary flow, an extension theorem of stationary flow and an extension theorem of nonnegative definite functions were proved. Moreover, we developed both the theory of weight transformation for degenerate flows in a vector space with a metric and the theory of nonlinear information analysis for local stochastic processes with discrete time. By using these results, we resolved the nonlinear prediction problem for onedimensional strictly stationary processes which had remained to be solved for a long time after MasaniWiener's work. Furthermore, by developing a nonlinear information analysis for local multidimensional stochastic processes with discrete time and then using the theory of linear prediction in the theory of KM_2OLangevin equa
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tions for degenerate flows, we solved both the nonlinear prediction problem and the nonlinear filtering problem for multidimensional stochastic processes with discrete time. As another application of the nonlinear information analysis for local multidimensional stochastic processes with discrete time, we introduced the concept of weak causality that is weaker than yhe one of strong causality investigated so far. Precisely speaking, for given two stochastic proceses X=(X(n) ; 0【less than or equal】n【less than or equal】N), Y=Y(n) ; 0【less than or equal】n【less than or equal】N), we say that there exists a weak causality from X to Y if there exist certain M_O (0【less than or equal】M_O【less than or equal】N) and Borel functions f_n (M_O【less than or equal】n【less than or equal】N) such that Y(n)=f_n(X(n), X(n1), ..., X(0), Y(n1), Y(n2), ..., Y(0))(M_O【less than or equal】n【less than or equal】N). Furthermore, by establishing a criteria of Test (CS) that determines the existence of weak causality from X to Y for given two time series data X=(X(n) ; 0【less than or equal】n【less than or equal】N), X=(X(n) ; 0【less than or equal】n【less than or equal】N), we investigated both th weak causality and the strong causality among the various time series data that are related to the E1 Nino phenomena that is said to be related to the increase of earth atmosphere temperature and announced their results at ICIAM99 that was held in Edinburg in 1999. We constructed another genarating system of the nonlinear information space by proving an approximation theorem by the radial basic functions that are used in the chaotic time series data. Moreover, we developed several softs that deterimine the stationarity, causality, determinicity and chaotic property of time series data and a unified soft that derives cetain dynamics behind time series data and then predicts its future. Thus, we can apply these softs to carry out causal analysis, model analysis and prediction analysis for time series data with the framework of the theory of KM_2OLangevin equations. Less
