In mathematics, a **stationary process** (or **strict(ly) stationary process** or **strong(ly) stationary process**) is a stochastic process whose joint probability distribution does not change when shifted in time or space. Consequently, parameters such as the mean and variance, if they exist, also do not change over time or position.

Stationarity is used as a tool in time series analysis, where the raw data are often transformed to become stationary; for example, economic data are often seasonal and/or dependent on a non-stationary price level. An important type of non-stationary process that does not include a trend-like behavior is the cyclostationary process.

Note that a "stationary process" is not the same thing as a "process with a stationary distribution". Indeed there are further possibilities for confusion with the use of "stationary" in the context of stochastic processes; for example a "time-homogeneous" Markov chain is sometimes said to have "stationary transition probabilities". On the other hand, all stationary Markov random processes are time-homogeneous.

Read more about Stationary Process: Definition, Examples

### Famous quotes containing the words stationary and/or process:

“It is the dissenter, the theorist, the aspirant, who is quitting this ancient domain to embark on seas of adventure, who engages our interest. Omitting then for the present all notice of the *stationary* class, we shall find that the movement party divides itself into two classes, the actors, and the students.”

—Ralph Waldo Emerson (1803–1882)

“... geometry became a symbol for human relations, except that it was better, because in geometry things never go bad. If certain things occur, if certain lines meet, an angle is born. You cannot fail. It’s not going to fail; it is eternal. I found in rules of mathematics a peace and a trust that I could not place in human beings. This sublimation was total and remained total. Thus, I’m able to avoid or manipulate or *process* pain.”

—Louise Bourgeois (b. 1911)