Stationary Processes

Stationary processes are stochastic processes whose probabilistic structure is unaffected by shifts in time. According to the interpretation of the term “probabilistic structure”, one distinguishes weak sense stationary processes, where only the covariance structure is supposed to be invariant, and strict sense stationary processes, for which all finitedimensional distributions have to remain the same under shifts of time. Some important basic properties are discussed, and the spectral representation of a stationary process and its relation to questions of linear prediction are studied.