Stationary Random Process

The concept of stationarity plays an important role in solving practical problems involving random processes. Just like time-invariance is an important characteristics of many deterministic systems, stationarity describes certain time-invariant property of a class of random processes. Stationarity also leads to frequency-domain description of a random process.

Strict-sense Stationary Process

A random process is called strict-sense stationary (SSS) if its probability structure is invariant with time. In terms of the joint distribution function, is called SSS if

Thus, the joint distribution functions of any set of random variables does not depend on the placement of the origin of the time axis. This requirement is a very strict. Less strict form of stationarity may be defined.

Particularly,

if then is called order stationary.

is called order stationary does not depend on the placement of the origin of the time axis. This requirement is a very strict. Less strict form of stationarity may be defined.