Introduction to Probability · Problem 11.2.5

Markov Chains — Grinstead & Snell

Mathematics — Probability · absorbing-markov-chains

Problem

For Example 11.11, verify that the following matrix is the inverse of

\mathbf{I} - \mathbf{Q}

and hence is the fundamental matrix

\mathbf{N}

\mathbf{N} = \begin{pmatrix} 8/3 & 1/6 & 4/3 & 2/3 \\ 4/3 & 4/3 & 8/3 & 4/3 \\ 4/3 & 1/3 & 8/3 & 4/3 \\ 2/3 & 1/6 & 4/3 & 8/3 \end{pmatrix}.

Find

\mathbf{Nc}

and

\mathbf{NR}

. Interpret the results.