### 7.4.24 Markov chains: markov

Given the transition matrix of a Markov chain, the markov command will compute characteristic features of the chain. If M is a transition matrix, then markov(M) will return the list of the positive recurrent states, the list of corresponding invariant probabilities, the list of other strong connected components, the list of probabilities of ending up in the sequence of recurrent states. For example, if you enter

markov([[0,0,1/2,0,1/2],[0,0,1,0,0],[1/4,1/4,0,1/4,1/4],[0,0,1/2,0,1/2],[0,0,0,0,1]])

you will get

[[4]],[[0,0,0,0,1]],[[3,1,2,0]],[[1],[1],[1],[1],[1]]