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Math Help - Markov Chain First Step Analysis Question

  1. #1
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    Markov Chain First Step Analysis Question

    Hi,

    If i am given a transition probability matrix (4x4) for a Markov chain and I am given the state I begin in, then how can I find the probability that the process will never visit a certain state.

    Thanks for the help!
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  2. #2
    Moo
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    Hello,

    By Kolmogorov's 0-1 law, this probability is always 0 or 1. (Or so I guess ^^)
    So you just have to see if the corresponding element of M^n is 0 or different from 0 for any n.

    (to do so, diagonalise the matrix and you'll have an easy computation for M^n : PD^nP^{-1}, where D is the diagonal matrix of eigenvalues, etc, etc...)
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