Introduction to Probability · Problem 11.1

Random Walks — Grinstead & Snell

Mathematics — Probability · markov-chains-mean-first-passage

Problem

Consider the Markov chain with transition matrix

\mathbf{P} = \begin{pmatrix} 1/2 & 1/2 \\ 1/4 & 3/4 \end{pmatrix}.

Find the fundamental matrix

\mathbf{Z}

for this chain. Compute the mean first passage matrix using

\mathbf{Z}