Past exam of the mathematics course of the University of Cambridge / 2008 / ii / Paper 3 / 25I / Solution

An irreducible continuous-time Markov chain is positive recurrent when the mean return time to a state is finite, and null recurrent when return occurs almost surely but the mean return time is infinite. For the nonexplosive chain here, whose rates are bounded, positive recurrence is equivalent to existence of a normalized stationary distribution. All rates are understood to be positive.