A study of identification problem for continuous model in phenomena of complex system based on the theory of Langevin equations from the viewpoint of the theory of stochastic processes

从随机过程理论的角度研究基于朗之万方程理论的复杂系统现象中的连续模型辨识问题

基本信息

批准号：
10440026
负责人：
OKABE Yasunori
金额：
$ 4.29万
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

As a preparation for the aim to investigate weakly stationary process with continuous time by using weakly stationary process with discrete time, we developed the theory of KM_2O-Langevin equations for degenerate flows in the three directioins of the analysis of local non-linear information space, the analysis of weight transformations and the linear prediction theory. By using these results, we resolved not only 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, but also both the non-linear prediction problem and the non-linear filtering problem for multi-dimensional stochastic processes with discrete time.On the other hand, we constructed Kubo noise associated with multi-dimensional stationary flow with continuous time in a Hilbert space.Next, by taking a procedure of scaling limits of KM_2O-Langevin data that determines the local stochastic difference equation (KM_2O-Langevin … More equation) describing the time evolution of weakly stationary process with discrete time, we derived KMO-Langevin data that determines the global stochastic difference equation (KMO-Langevin equation). Conversely, for a class of weakly stationary process with continuous time, we derived KM_2O-Langevin equation from KMO-Langevin equation, by using the idea of innovation method in the filtering theory. Thus, we could obtain the algorithm calculating the discrete and global characteristics from the discrete and local characteristics and prove the representaion theorem of outer matrix function for continuous case from the one for discrete case. Therefore, we have completed the derivation of the stochastic difference equation describing the time evolution of weakly stationary process with discrete time not only for local case, but also for global case.Moreover, for a class of weakly stationary process X=(X(t) ; t∈R), we define for each positive number ∈, we define a stochastic process X_∈=(X(n∈) ; n∈Z). Then, we investigated KMO(resp.KM_2O)-Langevin data that determines the dissipation term and the fluctuation term in KMO(resp.KM_2O)-Langevin equation describing the time evolution of the weakly stationary process X and certatin ∈-dependence of KMO(resp.KM_2O)-Langevin data that determines the dissipation term and the fluctuation term in KMO (resp.KM_<>O)-Langevin equation describing the time evolution of the weakly stationary process X_∈. In particular, we could represent KMO-Langevin data associated with X as a scaling limits with respect to ∈ of KMO-Langevin data associated with X_∈. Less

为了准备通过离散时间使用弱固定过程在连续时间内调查弱固定过程的准备，我们开发了对当地非线性信息空间分析的三个直接蛋白的KM_2O-LANGEVIN方程理论，分析权重转换和线性预测理论。通过使用这些结果，我们不仅解决了一维严格静止的过程的非线性预测问题，这些过程在Masani-Wiener的工作后很长一段时间都可以解决，而且还可以解决非线性预测问题，而且非线性预测问题和非线性过滤问题，用于多维的随机时间与其他零件的差异，我们在零件上构建了噪声，我们将杂物与其他杂物相关联，而噪声是噪声，又有噪音，这些杂物是噪音，又有噪音，又有噪音。 Hilbert Space.Next，通过采用缩放限制km_2o-langevin数据的程序，该过程确定了局部随机差方程（KM_2O-Langevin…更多方程式），描述了用离散时间来描述弱固定过程的时间演变，我们衍生了KMO-LANGEVIN数据，该数据衍生了全局随机差异方程（KMO-kmo-kmo-lange）。相反，对于连续时间的一类弱固定过程，我们通过在滤波理论中使用创新方法来从kmo-langevin方程中得出KM_2O-LANGEVIN方程。这就是我们可以从离散和局部特征中计算出离散和全局特征的算法，并证明从一个离散案例的连续情况下的外矩阵函数的表示理论。因此，我们已经完成了随机差方程的推导，这些方程描述了弱固定过程的时间演变，不仅在本地情况下，而且对于全局情况。 Then, we investigated KMO(resp.KM_2O)-Langevin data that determines the dissipation term and the fluctuation term in KMO(resp.KM_2O)-Langevin equation describing the time evolution of the weakly stationary process X and certatin ∈-dependence of KMO(resp.KM_2O)-Langevin data that determines the dissipation term and the fluctuation term in KMO （resp.km _ <> o）-langevin方程描述了弱静止过程x_∈的时间演变。特别是，我们可以代表与x关联的kmo-langevin数据，作为与x_∈关联的kmo-langevin数据的缩放限制。较少的