Equilibrium distribution of a continuous-time Markov chain ($\pi P(t)=\pi$)

An equilibrium probability row vector is invariant under every time transition matrix, and satisfies $\pi Q=0$ when generator sums are defined. A finite irreducible chain has a unique such distribution and all transition rows converge to it. With absorbing states, every probability mixture on the closed absorbing states is an equilibrium, and limiting rows are determined by absorption probabilities. For a jump chain with stationary weights ${\alpha }_i$ and positive holding rates ${\lambda }_i$, the corresponding time-stationary weights are proportional to ${\alpha }_i/{\lambda }_i$.