随机过程中的随机变量概念错误及纠正
首发时间:2022-05-11
摘要:本文以维纳过程定义为例,分析了随机过程理论在研究单个质点随机运动时,将质点位移与时间之间的数量关系抽象为随机变量的基本概念错误,以及使用描述大量质点空间位置分布的随机变量数字特征来刻画单个质点位移随时间变化规律的方法错误。本文将布朗粒子位移与时间之间的数量关系还原为时间函数,根据爱因斯坦"布朗粒子在不同时间间隔中的运动相互独立"的基本假设,从理论上证明了布朗运动的瞬时速度为白噪声过程,并基于白噪声样本函数重新定义了维纳过程,建立了可正确描述单个布朗粒子运动规律的样本函数模型。
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Conceptual Error and Correction of Random Variable in Stochastic Process
Abstract:Taking the definition of Wiener Process as an example, this paper analyzes the basic conceptual error of abstracting the quantitative relationship between particle displacement and time into random variable when studying the random motion of a single particle in Stochastic Process, and the wrong method of using the digital characteristics of random variable describing the spatial position distribution of a large number of particles to describe the variation law of single particle displacement with time. In this paper, the quantitative relationship between Brownian particle displacement and time is restored to a time function. According to Einstein\'s basic assumption that the motion of Brownian particles in different time intervals is independent of each other, it is proved theoretically that the instantaneous velocity of Brownian motion is a white noise process. Based on the white noise sample function, the Wiener Process is redefined, and a sample function model which can correctly describe the motion law of a single Brownian particle is established.Conceptual Error and Correction of Random Variable in Stochastic Process.
Keywords: random variable sample function Wiener Process;
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