\(X\left ( t\right ) \) is Stationary: If all its statistics do not change with shift of origin
\(X\left ( t\right ) \) is Wide Sense Stationary: If the mean is constant, and \(R_{x}\left ( t,t+\tau \right ) =R_{x}\left ( \tau \right ) \)
where autocorrelation \(R_{x}\left ( \tau \right ) \) is defined as \(E\left [ x\left ( t\right ) x^{\ast }\left ( t+\tau \right ) \right ] .\) Note, if \(X\left ( t\right ) \) is real, then \(R_{x}\left ( \tau \right ) \) is real and even
Note: \(R\left ( x\right ) \) must be WSS if it is ergodic\(.\)So ergodic process has constant mean.