- #1

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**[/B]

**[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****Any help would be great thanks.****[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.**
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