Let $(X_n)_{n \ge 0}$ be an irreducible time-homogeneous [Markov chain](/page/Markov%20Chain) on a countable state space $S$. The chain admits a stationary distribution if and only if some state, and hence every state, is positive recurrent. In that case the stationary distribution is unique, and for every $i \in S$, \begin{align*} \pi_i=\frac{1}{\mathbb E_i[T_i^+]}. \end{align*}