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==Stationary distributions==
A distribution <math>\pi</math> is a stationary distribution of the Markov chain with stochastic matrix <math>P</math> if and only if <math>\pi P = \pi</math>. This can be written as:<ref name="PRS"/>
:<math>\forall j\in \mathbb{S}: \sum_{i\in \mathbb{S}} \pi_i p_{ij} = \pi_j</math>.
This condition implies that <math>\pi P^n=\pi</math> and hence if the Markov chain <math>(X_n, n\in \mathbb{N})</math> has initial distribution <math>X_0 = \pi</math> then <math>X_n = \pi</math> (in distribution) for any <math>n\in\mathbb{N}</math>.<ref name="PRS"/>
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