Past exam of the mathematics course of the University of Cambridge / 2010 / ii / Paper 1 / 27I / b

For an irreducible, nonexplosive, positive recurrent continuous-time Markov chain on a countable state space, there is a unique equilibrium distribution $\pi$ andIn particular every finite irreducible chain has this convergence. Continuous time removes the discrete-time periodicity obstruction. Reducible finite chains instead converge according to absorption probabilities into their closed classes.