Definitions:

For a random process {x(t)}^*, mean value μ_x(t) and autocorrelation function R_x(t,t+τ) are given by

* the symbol { } is used to denote an ensemble of sample function.

Stationary:  μ_x(t) and R_x(t,t+τ) do not vary as time t varies, i.e., μ_x(t) = μ_x and R_x(t,t+τ) = R_x(τ).

• Weakly stationary

• Strongly stationary

Self-stationary: for the k^th same function, the sample properties μ_x(t,k) and R_x(t,t+τ,k) do not vary.