# Thread: Markov Chain First Step Analysis Question

1. ## Markov Chain First Step Analysis Question

Hi,

If i am given a transition probability matrix (4x4) for a Markov chain and I am given the state I begin in, then how can I find the probability that the process will never visit a certain state.

Thanks for the help!

2. Hello,

By Kolmogorov's 0-1 law, this probability is always 0 or 1. (Or so I guess ^^)
So you just have to see if the corresponding element of $M^n$ is 0 or different from 0 for any n.

(to do so, diagonalise the matrix and you'll have an easy computation for $M^n$ : $PD^nP^{-1}$, where D is the diagonal matrix of eigenvalues, etc, etc...)