A study on modeling and prediction for nonlinear phenomena from the viewpoint of the theory of stochastic processes

随机过程理论视角下的非线性现象建模与预测研究

• 批准号: 07459007
• 负责人: OKABE Yasunori
• 金额: $ 2.69万
• 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: 1995
• 资助国家: 日本
• 起止时间: 1995 至 1997
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-07459007/
• 关键词: KM _2 O-Langevin Equation; KM _2 O-Langevin Matrix; Stationary Flow; Fluctuation-Dissipation Theorem; Stationarity; Causality; Deterministic Property; Chaotic Property; KM_2O-ランジュヴァン方程式; KM_2O-ランジュヴァン行列; 実験数字; 定常解析; 因果解析; 予測解析; エントロピー解析; 決定

We have obtained four theoretical results about the theory of KM_2 O - Langevin equations : (1) We have characterized a notion of stationarity for pair of flows by the fluctuation-dissipation theorem which holds among KM_2 O-Langevin matrix associated with the pair of flows ; (2) For any given nonnegative definite matrix function R with Toeplitz condition, we have constructed a KM _2 O-Langevin matrix satisfying the fluctuation-dissipation theorem and then a stationary pair of flows with R its correlation matrix function by solving KM _2 O-Langevin equation ; (3). We have obtained all extensions of any given stationary flow and correlation matrix function ; (4) As an application of (3) we have obtained a new prediction formulaWe have obtained six results about an application of the theory concerned to time series analysis : (1) We have made a statistical basis of both the stationary test and the causal test strong ; (2) We have proposed a deterministic test to judge whether the time evolution of time series is deterministic ; (3) We have proposed a chaotic test to judge whether the time evolution of time series is chaotic ; (4) We have studied two time series of measles and chickenbox treated in Sugihara-May 's paper (Nature, 1990). From the viewpoint of the theory concerned, we have supported their results based upon the chaotic time series analysis, by showing that both the time series behave determinately ; the former is chaotic and the latter is not so ; (5) We have obtained a theoretical method to estimate the deterministic dynamics describing the time evolution of time series after passing the deterministic test ; (6)As an application of (5), we have given an answer for the estimation problem of embeding dimension in chaotic time series analysis.

我们已经获得了有关KM_2 O- langevin方程理论的四个理论结果：（1）我们通过波动散文定理表征了一对流的平稳性概念，该定理在km_2 o-langevin矩阵之间存在于km_2 o-langevin矩阵之间； （2）对于任何具有Toeplitz条件的给定的非负定矩阵函数r，我们已经构造了满足波动散文定理的km _2 o-langevin矩阵，然后通过求解km _2 o-langevin equation s; （3）。我们已经获得了任何给定的静止流量和相关矩阵函数的所有扩展； （4）作为（3）的应用，我们获得了一个新的预测公式，从相关理论应用于时间序列分析中的应用六个结果：（1）我们已经对固定测试和因果测试的统计基础强劲; （2）我们提出了一项确定性测试，以判断时间序列的时间演变是否确定性； （3）我们提出了一次混乱的测试，以判断时间序列的时间演变是否混乱； （4）我们研究了在Sugihara-May的论文中处理的两个时间系列的麻疹和鸡盒（Nature，1990）。从相关理论的角度来看，我们根据混乱的时间序列分析来支持他们的结果，表明两个时间序列的表现都确定。前者是混乱的，后者不是这样。 （5）我们获得了一种理论方法来估计通过确定性测试后时间序列的时间演变的确定性动力学； （6）作为（5）的应用，我们为混乱时间序列分析中嵌入维度的估计问题提供了答案。

项目成果

Y.Okabe(with Y.Kiho,Y.Okada and others): "Functional Word in a Protein III.Syntax and Energetics" Proceedings of the Japan Academy. 72巻. 95-100 (1996)

Y.Okabe（与 Y.Kiho、Y.Okada 等人）：“蛋白质中的功能词 III. 语法和能量学”，日本科学院院刊，第 72 卷，95-100（1996 年）。

Y.Kiho, R.Yamada, Y.Okabe, C.Palmer and Y.Okada: ""Application of the Jellyfich model I : virulency of some mammalian viruses"" Proc.Japan Academy. Vol.73 No.8 Ser.B.170-175 (1997)

Y.Kiho、R.Yamada、Y.Okabe、C.Palmer 和 Y.Okada：““Jellyfich 模型 I 的应用：某些哺乳动物病毒的毒力””Proc.Japan Academy。

Y.Kiho, T.Iwai, Y.Okada, Y.Okabe, M.Ochi and K.Katori:""Functional word in a protein III;syntax and energtics"" Proc.Japan Academy. Vol.72,Ser.B,No.5. 95-100 (1996)

Y.Kiho、T.Iwai、Y.Okada、Y.Okabe、M.Ochi 和 K.Katori：“蛋白质中的功能词 III；语法和能量学”Proc.Japan Academy。

Y.Kiho, A.Ubasawa, Y.Okabe and T.Iwai: "" Functional word in a protein IV.alphabet" Proc.Japan Academy.Vol.72, Ser.B.No.9. 185-190 (1996)

Y.Kiho、A.Ubasawa、Y.Okabe 和 T.Iwai：“蛋白质 IV.alphabet 中的功能词”Proc.Japan Academy.Vol.72，Ser.B.No.9.185-190 (1996)

有本 卓: "Quasi-natural potential,passivity and learrability in robot dynamics with or without geometric constraint of system fluctuations" Proc.of The IIAS Workshop of Mathematical Approach to Fluctuations,Complexity,and Nonlinearity(ed.by T.Hida),. 48-83 (

Takashi Arimoto：“具有或不具有系统波动几何约束的机器人动力学中的准自然势、被动性和可学习性”Proc.of The IIAS Workshop of Mathematical Approach to Flutuations, Complexity, and Nonlinearity（由 T.Hida 编辑），。 48-83（