What is the general way of finding a probability that Markov chain goes to absorbing state

22 Views Asked by At

Given an NxN matrix like the on shown here: $$ \mathbf{M} = \matrix{~ \\ & 0 & 0.5 & 0 & 0 & 0 & 0.5\\ & 0.5 & 0 & 0 & 0.3 & 0.2 & 0 \\ & 0 & 0 & 1 & 0 & 0 & 0\\ & 0 & 0 & 0 & 1 & 0 & 0\\ & 0 & 0 & 0 & 0 & 1 & 0\\ & 0 & 0 & 0 & 0 & 0 & 1 } $$ What is the general way of finding the probability of going from state_0 (represented by first row) into each absorbing state (s2, s3, s4, s5 in this case) for any NxN matrix, if it is guaranteed that the matrix will have at least one absorbing state?