In mathematics and statistics, a stationary process is a stochastic process whose joint probability distribution does not change when shifted in time.

**STATIONARY PROCESS:**

In
mathematics and statistics, a stationary process is a stochastic process whose
joint probability distribution does not change when shifted in time.
Consequently, parameters such as the mean and variance, if they are present,
also do not change over time and do not follow any trends.

Stationary
is used as a tool in time series analysis, where the raw data is 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 behaviour 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". Besides, all
stationary Markov random processes are time-homogeneous.

^{ü} **Definition:**

^{ü} **Wide Sense Stationary:**

Weaker
form of stationary commonly employed in signal processing is known as
weak-sense stationary, wide-sense stationary (WSS), covariance stationary, or
second-order stationary. WSS random processes only require that 1st moment and
covariance do not vary with respect to time. Any strictly stationary process
which has a mean and a covariance is also WSS.

So, a
continuous-time random process x(t) which is WSS has the following restrictions
on its mean function.

and auto
covariance function.

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Communication Theory : Random Process : Stationary Process |

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