Stationary distribution may refer to:

• The limiting distribution in a Markov chain
• The marginal distribution
  Marginal distribution
  In probability theory and statistics, the marginal distribution of a subset of a collection of random variables is the probability distribution of the variables contained in the subset. The term marginal variable is used to refer to those variables in the subset of variables being retained...
  
   of a stationary process
  Stationary process
  In the mathematical sciences, a stationary process is a stochastic process whose joint probability distribution does not change when shifted in time or space...
  
   or stationary time series
  Time series
  In statistics, signal processing, econometrics and mathematical finance, a time series is a sequence of data points, measured typically at successive times spaced at uniform time intervals. Examples of time series are the daily closing value of the Dow Jones index or the annual flow volume of the...
  
  
• The set of joint probability distributions of a stationary process
  Stationary process
  In the mathematical sciences, a stationary process is a stochastic process whose joint probability distribution does not change when shifted in time or space...
  
   or stationary time series
  Time series
  In statistics, signal processing, econometrics and mathematical finance, a time series is a sequence of data points, measured typically at successive times spaced at uniform time intervals. Examples of time series are the daily closing value of the Dow Jones index or the annual flow volume of the...
  
  

In some fields of application, the term stable distribution is used for the equivalent of a stationary (marginal) distribution, although in probability

Probability

Probability is ordinarily used to describe an attitude of mind towards some proposition of whose truth we arenot certain. The proposition of interest is usually of the form "Will a specific event occur?" The attitude of mind is of the form "How certain are we that the event will occur?" The...

 and statistics

Statistics

Statistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....

 the term has a rather different meaning: see stable distribution.

Crudely stated, all of the above are specific cases of a common general concept. A stationary distribution is a specific entity which is unchanged by the effect of some matrix or operator: it need not be unique. Thus stationary distributions are related to eigenvectors for which the eigenvalue is unity.

See also

• Stationary ergodic process
  Stationary ergodic process
  In probability theory, stationary ergodic process is a stochastic process which exhibits both stationarity and ergodicity. In essence this implies that the random process will not change its statistical properties with time and that its statistical properties can be deduced from a single,...
  
  
• Perron–Frobenius theorem
• Stationary state
  Stationary state
  In quantum mechanics, a stationary state is an eigenvector of the Hamiltonian, implying the probability density associated with the wavefunction is independent of time . This corresponds to a quantum state with a single definite energy...
  
   or ground state
  Ground state
  The ground state of a quantum mechanical system is its lowest-energy state; the energy of the ground state is known as the zero-point energy of the system. An excited state is any state with energy greater than the ground state...
  
  in quantum mechanics