Time series analysis for abnormality test and modeling of corrplex system and a study for the derived model from a view point of the theory of stochastic processes

随机过程理论视角下复杂系统异常测试与建模的时间序列分析及推导模型研究

基本信息

批准号：
14340030
负责人：
OKABE Yasunori
金额：
$ 5.82万
依托单位：
The 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：
2002
资助国家：
日本
起止时间：
2002 至 2004
项目状态：
已结题

项目摘要

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.

我们通过使用KM_2O-LANGEVIN方程的理论，获得了在两个离散时间随机过程之间计算两个离散时间随机过程之间非线性滤波器的公式。 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 obtaining an algorithm for calculating the non-linear fiter, which had been unsolved since Kalman-Bucy's work.By defining the absoluteness of time series as the degree of breakdown of stationarity of time series, we have proposed Test(ABN) for catching certain signs of the通过使用测试测试时间序列的平稳性和多项式类型的生成系统，用于非线性信息空间，与离散时间随机过程有关的多项式类型的生成系统。通过应用测试（ABN）和测试（d）测试时间序列的时间序列，我们已经发现了一个地震，Aurora和大脑的属性，我们已将时间序列确定为新的属性，我们已经发现了新的属性，我们已经发现了新的质量，我们已经在范围内发现了一个质量，我们已经发现了新的质量，我们已经发现了新的属性，我们已经在新的属性中，对新的属性，我们已将其确定为新的质量，以使新的属性属于新的属性，从S波到达深度低频地震，Aurora的发生以及具有ECOG平稳性的总区域后的平稳性。这种分离特性并未出现在通常的地震和EEG中。通过处理连续的时间固定过程X，其全球时间演变受[α，β，γ] - 倾斜度方程的支配，我们均得出了连续的时间KM_2O-LANGEVIN，从而描述了局部时间进化的局部时间进化以及表现出coefferation exse e sosefors coeffers coeffers coeffere的局部时间进化。