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.

本文得到了关于KM_2 O-Langevin方程理论的四个结果：（1）利用与流偶有关的KM_2 O-Langevin矩阵的涨落耗散定理，刻画了流偶的平稳性概念;（2）对任意给定的满足Toeplitz条件的非负定矩阵函数R，通过求解KM_2 O-Langevin方程，构造了一个满足涨落耗散定理的KM_2 O-Langevin矩阵，进而构造了一个以R为相关矩阵函数的定常流对;（4）作为（3）的应用，我们得到了一个新的预报公式。我们得到了有关理论在时间序列分析中的应用的六个结果：（1）我们使平稳检验和因果检验的统计基础都很强;（2）提出了判断时间序列时间演化是否确定的确定性检验方法：（3）提出了判断时间序列时间演化是否混沌的混沌性检验方法;（4）我们研究了Sugihara-May的论文（Nature，1990）中所处理的麻疹和鸡痘的两个时间序列。从理论上支持了他们基于混沌时间序列分析的结果，证明了两个时间序列的行为都是确定的，前者是混沌的，而后者不是混沌的.（5）给出了一种理论方法来估计通过确定性检验后描述时间序列时间演化的确定性动力学;（6）作为（5）的应用，我们给出了混沌时间序列分析中嵌入维数估计问题的一个解答。

项目成果

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)

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.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.Okabe: "Non-linear time series analysisbased upon the fluctuation-dissipationthe-orem" Proceedings of The Second WorldCongress of Nonlinear Analysists. (1996)

Y.Okabe：“基于波动耗散定理的非线性时间序列分析”第二届世界非线性分析大会论文集。