The long-run behavior of Markov chains

AbstractWe study the long-run behavior of the finite Markov chains by investigating the limiting spaces of the n-step possibility distributions, which are shown always to exist. Let P be an n × n Markov matrix, and put xi = Pi(x0), i = 1, 2, 3, …, where x0 is any initial possibility distribution. We find that the set of the limiting points of {xi} either contains a unique steady-state distribution or equals a unique orbit of a periodic-state distribution