Development of unified system with non-linear analytic technique for time series data based upon the fluctuation-dissipation theorem

基于波动耗散定理的时间序列数据非线性分析技术统一系统的开发

基本信息

批准号：
10554001
负责人：
OKABE Yasunori
金额：
$ 8.13万
依托单位：
University of Tokyo
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (B).
财政年份：
1998
资助国家：
日本
起止时间：
1998 至 2000
项目状态：
已结题

项目摘要

We constructed a theory of KM_2O-Langevin equations for flows in a vector space with a metric in which a characterization theorem that characterizes stationarity of flow in terms of the fluctuation-dissipation theorem, a construction theorem of stationary flow, an extension theorem of stationary flow and an extension theorem of non-negative 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 non-linear information analysis for local stochastic processes with discrete time.By using these results, we resolved the non-linear prediction problem for one-dimensional strictly stationary processes which had remained to be solved for a long time after Masani-Wiener's work. Furthermore, by developing a non-linear information analysis for local multi-dimensional stochastic processes with discrete time and then using the theory of linear prediction in the theory of KM_2O-Langevin equa … More tions for degenerate flows, we solved both the non-linear prediction problem and the non-linear filtering problem for multi-dimensional stochastic processes with discrete time.As another application of the non-linear information analysis for local multi-dimensional 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(n-1), ..., X(0), Y(n-1), Y(n-2), ..., 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 non-linear 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_2O-Langevin equations. Less

我们构建了一种具有度量的向量空间中的流量的KM_2O-兰格方程理论，在该矢量空间中，表征理论表征了流动静止理论的流动平稳性，一种平稳流的构建理论，平稳流动的延伸理论和非阴性定义功能的扩展理论。此外，我们既开发了具有指标的媒介空间中退化流量的重量转化理论，也开发了具有离散时间的本地随机过程的非线性信息分析的理论。通过这些结果，我们解决了对一维严格的平稳过程的非线性预测问题，这些过程已在Masani-Wienerer的工作中得到了很长时间的解决。 Furthermore, by developing a non-linear information analysis for local multi-dimensional stochastic processes with discrete time and then using the theory of linear prediction in the theory of KM_2O-Langevin equi… More terms for degenerate flows, We solved both the non-linear prediction problem and the non-linear filtering problem for multi-dimensional stochastic processes with discrete time.As another application of the non-linear information analysis for local随着离散时间的多维随机过程，我们引入了弱因果关系的概念，该概念比迄今为止所研究的强大因果关系弱。准确地说，对于给定的两个随机过程x =（x（n）; 0 [小于或相等] n [小于或小于或相等] n），y = y（n）; 0【小于或等于】n【小于或等于】n n），我们说，如果存在某些M_O（0小于或等于或等于】n），则从x到y的差异很弱，而borel函数却小于或等于或等于或等于或等于或等于或等于或等于或等于n n n n n n n n n n n n n n n n n n n n n】n（x）（x）。 x（n-1），...，x（0），y（n-1），y（n-2），...，y（0））（m_o【小于或等于】n【小于或等于】n）。此外，通过建立一个测试标准（CS），该标准决定了两个时间序列数据的因果关系弱的因果关系弱的因果关系x =（x（n）; 0小于或等于或等于】n【小于或等于或等于或等于】nn】n。 atmosphere temperature and announced their results at ICIAM99 that was held in Edinburg in 1999.We constructed another genarating system of the non-linear information space by providing an approximation theorem by the radial basic functions that are used in the chaotic time series data.Moreover, we developed several softs that determine the stationarity, causality, determining and chaotic property of time series data and a unified soft that derives cetain dynamics behind time series data and then预测它的未来。较少的