Grinstead-Snell-Probability · Problem 11.4.3

Markov Chains

Mathematics · fundamental-limit-theorem-fixed-vectors

Problem

Let

\mathbf{P} = \begin{pmatrix} 1 & 0 & 0 \\ .25 & 0 & .75 \\ 0 & 0 & 1 \end{pmatrix}

be a transition matrix of a Markov chain. Find two fixed vectors of

\mathbf{P}

that are linearly independent. Does this show that the Markov chain is not regular?