Solution
= Solution
For an irreducible, nonexplosive, positive recurrent <continuous-time Markov chain> on a countable state space, there is a unique equilibrium distribution $\pi$ and
$$
\boxed{P_{ij}(t)\longrightarrow\pi_j\quad(t\to\infty).}
$$
In 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.