Given a_j⁽⁰⁾ and P of a Markov chain, the absolute probabilities of the system after a specified number of transitions are determined as follows.
Let a_j⁽ⁿ⁾ be the absolute probabilities of the system after n transitions, that is, at t_n. The general expression a_j⁽ⁿ⁾ in terms of a_j⁽⁰⁾ and P can be found as follows.