随机过程定义的逻辑结构缺陷及完善
首发时间:2022-06-28
摘要:本文指出了现有随机过程定义只有"属概念"而无"种差"的逻辑结构缺陷。现有随机过程定义只给出了描述随机过程的二元函数"属概念",并未给出反映随机过程本质属性和数量关系的"种差",因此无法准确揭示随机过程概念的内涵与外延。本文对抛硬币试验结果产生的随机时间序列进行了数量分析,抽象出了"零均值"和"不相关"这两个重要的随机性本质属性与数量关系,用白噪声和算子构造出了反映随机过程本质属性和数量关系的"种差",给出了具有"属概念"和"种差"结构的随机过程定义。
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Logical Structure Defect and Perfection of Stochastic Process Definition
Abstract:This paper points out that the existing definition of stochastic process has only " genus concept" but no "specific difference " logical structure defect. The existing stochastic process definition only gives the " genus concept" of the binary function describing the stochastic process, but does not give the "species difference" that reflects the essential properties and quantitative relationship of the stochastic process, so it is impossible to accurately reveal the connotation and extension of the concept of stochastic process. . This paper makes a quantitative analysis of the random time series generated by the results of the coin tossing test, abstracts two important random essential properties and quantitative relationships, namely "zero mean" and " uncorrelation ", and uses white noise and operator to construct a The "species difference" which reflects the essential properties and quantitative relationship of random process, gives the definition of stochastic process with "genus concept" and "species difference" structure.
Keywords: randomness white noise frequency domain analysis;
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