= Solution
An <equilibrium distribution of a continuous-time Markov chain> is a probability row vector $\pi$ invariant under the transition semigroup: $\pi P(t)=\pi$ for every $t\geq0$. Differentiating gives $\pi Q=0$, or $\sum_i\pi_iq_{ij}=0$ for each $j$, when the generator sums are defined. Reducible chains may have several closed classes supporting different equilibrium distributions; convex mixtures are then also equilibria. Irreducibility and positive recurrence give uniqueness for a conservative nonexplosive chain.
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