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Answers for “如何找到马尔可夫链的平稳分布?”

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The stationary distribution is the row vector π=[4/11,7/11]\pi = [4/11, 7/11].

Conditions: The transition matrix is P=[0.30.70.40.6]P = \begin{bmatrix} 0.3 & 0.7 \\ 0.4 & 0.6 \end{bmatrix}.; π\pi is a row vector satisfying πP=π\pi P = \pi and ∑πi=1\sum \pi_i = 1.

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A stationary distribution (also called an invariant distribution) is a probability distribution row vector π\pi that remains unchanged when multiplied by the transition matrix PP 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: π\pi is a row vector.; PP is the transition matrix of the Markov chain.; The elements of π\pi are non-negative and sum to 1.