Consider the four state Markov chain {0, 1, 2, 3} whose transition probability matrix is given by P
P =
1.0 0.0 0.0 0.0
0.1 0.2 0.5 0.2
0.1 0.2 0.6 0.1
0.0 0.0 0.0 1.0
Q =
1 2
0 0.2 0.5
1 0.2 0.6
and the transition probability matrix corresponding to the non absorbing states Q. Calculate the matrix inverse to I - Q and from this calculate the probability of absorption into space 0 starting from state 1 and the mean time spent in each of states 1 and 2 prior absorption.