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I have 9 x 9 Markov chain state transition matrix. There are 5 states which are visited just once, and then the chain iterates through the remaining 4 states indefinitely. I have calculated the eigenvalues and eigenvectors of $\mathbf{T}$. Of the remaining 4 states, 2 are special. I would like to find the probability that there are $n$ consecutive visits to the special states. How can I find this probability?

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  • $\begingroup$ Do you know the transition probabilities? $\endgroup$ Jul 30, 2017 at 18:11
  • $\begingroup$ The 4 states must have 0 probability transitioning to the other 5, so you have a block matrix where you can fix quite many 0s in it. $\endgroup$ Jul 30, 2017 at 19:01
  • $\begingroup$ Yes, I know the transition probabilities between the 4 states $\endgroup$
    – mmh
    Jul 30, 2017 at 21:09

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