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

 

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

\begin{bmatrix}  0.0 & 0.0 &1.0 \\  0.0 & 1.0 & 0.0\\  0.0& 0.0 & 1.0  \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} = 0.0

p_{22} = 1.0

p_{33} = 1.0

Since p_{22} and p_{33} equal 1, state 2 and 3 are absorbing state.

 

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