Stationary Process

Topics: Types of Stochastic Processes

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(definition)

We say a stochastic process is a stationary process when, for any $t_1,t_2,\dots ,t_n$ (state set), the probability distribution of the vector $\left(X_t,X_{t_2},\dots ,X_{t_n}\right)$ is the same one for $\left(X_{t_1+h},X_{t_2+h},\dots ,X_{t_n+h}\right)$, for any $h>0$.

In other words, the distribution of the vector of random variables is the same for any value of $t$.