Process

Overview

In probability, a process is a random variable that evolves over time. As an example, a stock price would be considered a stochastic process. From this perspective, one could view the value of price at each time as a separate random variable. That is {% price_t %} is a random variable, and {% price_{t+1} %} is a separate random variable.

Formal Definition

For a fixed sample point {% \omega %} of the given space of points {% \Omega %} A stochastic process is a function {% t \rightarrow X_t(\omega) %}. That is, each sample point is a function of time.

Measure Theory Formalities