Find the absorbing state(s) for the transition matrix shown

Find the absorbing state(s) for the transition matrix shown.

\begin{bmatrix}  1.0 & 0.0 &0.0 \\  1.0 & 0.0 & 0.0\\  0.3& 0.7 & 0.0  \end{bmatrix}

 

Solution

 

A state is an absorbing state of  a Markov chain if p_{ii} = 1. Thus, check the entries p_{11}, p_{22}, and p_{33} to see if any of them are equal to 1.

p_{11} = 1.0

p_{22} = 0.0

p_{33} = 0.0

Since p_{11} equal 1, state 1 is the absorbing state.

 

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