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Math Help - Markov Chain problem.

  1. #1
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    Cool Markov Chain problem.

    With two-state Markov chain which a one-step transition matrix :

    P = [ 7/8 1/8 ]
    [ 1/8 7/8 ]

    How would i find the eigenvalues of P and derive an explicit expression for Pn?.
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    Quote Originally Posted by harrybarryt View Post
    How would i find the eigenvalues of P and derive an explicit expression for Pn?.

    The eigenvalues of P are \lambda_1=1,\;\lambda_2=3/4 and the corresponding eigenvectors

    v_1=(1,1),\;v_2=(-1,1)

    so,

    P^r=\begin{bmatrix}{1}&{-1}\\{1}&{\;\;\;1}\end{bmatrix}\begin{bmatrix}{1^r}  &{0}\\{0}&{(3/4)^r}\end{bmatrix}\begin{bmatrix}{1}&{-1}\\{1}&{\;\;\;1}\end{bmatrix}^{-1}=\ldots
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