随机过程的概念解析

The Mathematical Analysis of the Concept of Stochastic Process

通过分析Bernoulli试验对应的随机变量序列,给出随机过程的直观定义导致的矛盾.借助测度论的基本概念系统,解析随机过程的数学定义,给出随机过程样本函数与随机过程实现的概念一致性.

By the analysis of Bernoulli experiment, the intuitive definition of stochastic process resulted in a contradiction with the sequence of Bernoulli random variables. With the measure theory, the concept of stochastic process could be mathematical defined, and the concept of sample function could be identified with the concept of the implementation of stochastic process.