随机过程定义的逻辑结构缺陷及完善  

The Logical Structure Defect and Perfection of Stochastic Process Definition

作　　者：高宏[1] GAO-Hong(Department of Precision Instrument,Tsinghua University,Beijing 100084,China)

机构地区：[1]清华大学精密仪器系,北京海淀100084

出　　处：《汉江师范学院学报》2023年第6期1-5,共5页Journal of Hanjiang Normal University

摘　　要：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.通过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.This paper points out the logical structure defect that the existing definition of stochastic process only has"genus concept"but no"species difference",which only gives the binary function"genus concept"to describe stochastic process,but does not give the"species difference"to reflect the essential attributes and quantitative relations of stochastic process,so it cannot accurately reveal the connotation and extension of the concept of stochastic process.In this paper,a quantitative analysis of the random time series produced by the result of the coin toss experiment is carried out,and two important intrinsic properties and quantitative relations of randomness,"zero mean"and"uncorrelated",are abstracted.By using white noise and operators,a"variety"reflecting the intrinsic properties and quantitative relations of random processes is constructed,and the definition of random processes with the structure of"genus concept"and"variety"is given.

关 键 词：随机性 白噪声 频域分析 

分 类 号：O211.6[理学—概率论与数理统计]