A discrete time stochastic process is a sequence of random variables \[X_1, X_2, \dots\]

Stochastic means random. The indices of the random variables are thought of as time indexes. So, the value of \(X_5\) represents the value of the process at time \(5.\)

The sequence of the closing prices of a stock at the end of each day the stock market is open is a discrete time stochastic process. It may look something like this: \begin{align} & X_1 = 12.91 \\ & X_2 = 12.80 \\ & X_3 = 13.01 \\ & \dots \end{align}

Current temperature is not a discrete time stochastic process. Instead, it is real time. Such a process is called a continuous time stochastic process. For example, if we let \(t = 0\) represent noon today and let time be measured in seconds, then \(X_{7.8}\) means the temperature exactly \(7.8\) seconds after noon. There would be a random variable \(X_t\) for every time \(t \in [0,\infty).\)