随机过程研究方法的逻辑错误及纠正
首发时间:2021-09-29
摘要:随机过程明确定义样本函数x(t)和随机变量X(t)是两个定义域与值域完全不同的函数,并将随机运动的质点在t时刻的位移x(t)抽象为随机过程X(ω,t) 固定ω时的一个样本函数。但是,随机过程理论在推导证明样本函数x(t)的性质时,却用随机变量X(t)替换了样本函数x(t),导致物理研究对象从单个质点改变为质点集合,因而只能用刻画质点集体行为的统计规律来描述单个质点的个体行为。本文分析了随机过程研究方法混淆样本函数和随机变量基本概念、违反同一律的逻辑错误,以及由此产生的理论与经验事实不符、理论内部出现逻辑悖论等反常问题。
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Logical Error and Correction in Research Method of Stochastic Processes
Abstract:The Random Processes clearly defines the sample function x(t) and the random variable X(t) as two functions with completely different definition domains and value field, and the displacement x(t) of a random moving particle at time t is abstracted as a sample function of a random process X(ω,t) when ω is fixed. However, when deriving and proving the properties of sample function x(t), The Random Processes replaces the sample function x(t) with a random variable X(t), which causes the physical research object to change from a single particle to a set of particles. Therefore, the individual behavior of a single particle can only be described by the statistical characteristics describing the collective behavior of particles. This article analyzes the random process research methods that confuse the basic concepts of sample functions and random variables, the logical errors that violate the law of identity, and the resulting inconsistencies between theories and empirical facts, and the ogical paradox in the Random Processes theory.
Keywords: random processes sample function random variable
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