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bonfire09
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Homework Statement
For the following Markov chain, find the rate of convergence to the stationary distribution:
[itex] \begin{bmatrix} 0.4 & 0.6 \\ 1 & 0 \end{bmatrix} [/itex]
Homework Equations
none
The Attempt at a Solution
I found the eigenvalues which were [itex] \lambda_1=-.6 [/itex] or [itex] \lambda_2=1 [/itex]. The corresponding eigenvectors I found were [itex] \vec{v_1}=\begin{bmatrix} -0.6 & 1 \end{bmatrix}[/itex] and [itex] \vec{v_2}=\begin{bmatrix} -1 & 1 \end{bmatrix} [/itex]. The stationary distribution which I found that satisfies [itex] p=pA [/itex](A is the transition matrix) and [itex]p_1+p_2=1[/itex] is [itex] \vec{p}=\begin{bmatrix} .625 & .375 \end{bmatrix} [/itex]. From here I do not know how to get the rate of convergence. I think it has something to do with the eigenvalues or eigenvectors. Any help would be great thanks.[/B]
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