In probability theory - specifically in the theory of stochastic processes, a stationary sequence is a random sequence whose joint probability distribution is invariant over time. If a random sequence X j is stationary then the following holds:
\begin{align} &{}
| F | |
| Xn,Xn+1,...,Xn+N-1 |
(xn,xn+1,...,xn+N-1)\\ &=
| F | |
| Xn+k,Xn+k+1,...,Xn+k+N-1 |
(xn,xn+1,...,xn+N-1), \end{align}
where F is the joint cumulative distribution function of the random variables in the subscript.
If a sequence is stationary then it is wide-sense stationary.
If a sequence is stationary then it has a constant mean (which may not be finite):
E(X[n])=\mu foralln.