Stationary Distribution

Stationary distribution may refer to:

  • The limiting distribution in a Markov chain
  • The marginal distribution of a stationary process or stationary time series
  • The set of joint probability distributions of a stationary process or stationary time series

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

Read more about Stationary DistributionSee Also

Other articles related to "stationary distribution, distribution, stationary":

Markov Logic Network - Inference
... in a Markov logic network is to find the stationary distribution of the system, or one that is close to it that this may be difficult or not always possible is illustrated by the richness ... As in a Markov network, the stationary distribution finds the most likely assignment of probabilities to the vertices of the graph in this case, the vertices are the ground ... That is, the distribution indicates the probability of the truth or falsehood of each ground atom ...
Fork-join Queue - Stationary Distribution - Heavy Traffic/diffusion Approximation
... process can be approximated by a reflected Brownian motion which converges to the same stationary distribution as the original queueing process ...
Stationary Distribution - See Also
... Stationary ergodic process Perron–Frobenius theorem Stationary state or ground state in quantum mechanics ...
Markov Chain - Finite State Space - Convergence Speed To The Stationary Distribution
... As stated earlier, from the equation, (if exists) the stationary (or steady state) distribution π is a left eigenvector of row stochastic matrix P ... If there is a unique stationary distribution, then the largest eigenvalue and the corresponding eigenvector is unique too (because there is no other π which ... left and continue this operation with the results, in the end we get the stationary distribution π ...

Famous quotes containing the words distribution and/or stationary:

    Classical and romantic: private language of a family quarrel, a dead dispute over the distribution of emphasis between man and nature.
    Cyril Connolly (1903–1974)

    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)