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A stationary distribution (also called an invariant distribution) is a probability distribution row vector $\pi$ that remains unchanged when multiplied by the transition matrix $P$ of a Markov chain. This means that if the system starts in this distribution, it will remain in this distribution at all future time steps.

Conditions: $\pi$ is a row vector.; $P$ is the transition matrix of the Markov chain.; The elements of $\pi$ are non-negative and sum to 1.

A stationary distribution (also called an invariant distribution) is a probability distribution row vector $\pi$ that remains unchanged when multiplied by the transition matrix $P$ of a Markov chain. This means that if the system starts in this distribution, it will remain in this distribution at all future time steps.

Conditions: $\pi$ is a row vector.; $P$ is the transition matrix of the Markov chain.; The elements of $\pi$ are non-negative and sum to 1.