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I have given the stationary distribution $\pi=(1/9,3/4,5/36)$ of a connected Markov chain, which I don‘t know. Is it possible to generate the transition probability matrix of a Markov chain that has this stationary distribution?

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    $\begingroup$ There are 9 unknowns and only 5 equations. $\endgroup$ Commented Jul 31, 2020 at 17:12

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Take a look at the Metropolis-Hastings algorithm

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