Introduction to Probability · Problem 11.2.6

Markov Chains — Grinstead & Snell

Mathematics — Probability · absorbing-markov-chains

Problem

In the Land of Oz example (Example 11.1), change the transition matrix by making R an absorbing state. This gives

\mathbf{P} = \begin{array}{c} R \\ N \\ S \end{array} \begin{pmatrix} 1 & 0 & 0 \\ 1/2 & 0 & 1/2 \\ 1/4 & 1/4 & 1/2 \end{pmatrix}.

Find the fundamental matrix

\mathbf{N}

, and also

\mathbf{Nc}

and

\mathbf{NR}

. Interpret the results.