An irreducible nonexplosive <continuous-time Markov chain> has an equilibrium probability distribution exactly when it is positive recurrent. The distribution is unique, and gives the long-run fraction of elapsed time in each state. A null recurrent chain has no equilibrium probability distribution. The finite one-state absorbing case is trivially stationary; the return-cycle descriptions concern nontrivial irreducible classes.

Solution

Past exam of the mathematics course of the University of Cambridge / 2010 / ii / Paper 4 / 26I / a / Solution

 Solution (source code)