随机过程理论中的三个基本概念错误

随机过程是揭示和探讨客观世界动态随机现象数量关系及其变化规律的应用数学理论。文章分析随机过程理论在研究质点随机运动时,将质点位移与时间之间的数量关系抽象为随机变量,并用描述大量重复试验中随机事件发生可能性的概率来度量随机游走每一步向右或向左的可能性大小,以及将随机过程样本函数当作随机变量等基本概念错误。随机过程理论中出现的基本概念错误不仅导致随机过程样本轨道研究对象发生错位,而且也为自然科学、工程技术和社会科学提供错误的理论、方法及工具。

Stochastic process is an applied mathematical theory that reveals and discusses the quantitative relationship and changing laws of dynamic random phenomena in the objective world. This paper analyzes the random process theory when studying the random movement of the particle, abstracting the relationship between the displacement of the particle and time as a random variable, and measuring the possibility of right or left in each step of random walk by the probability of a random event occurring in a large number of repeated trials, and treats the sample function of random process as a random variable.The basic conceptual errors in the stochastic process not only lead to the dislocation of the research object of random process sample path, but also provide wrong theories, methods and tools for natural sciences, engineering technology and social sciences.