NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, VOL.18, PP.931-946, 2011. TITLE: Bounding the equilibrium distribution of Markov poupulation models AUTHORS: Tugrul Dayar, Holger Hermanns, David Spieler, and Verena Wolf ABSTRACT: We propose a bounding technique for the equilibrium probability distribution of continuous-time Markov chains with population structure and infinite state space. We use Lyapunov functions to determine a finite set of states that contains most of the equilibrium probability mass. Then we apply a refinement scheme based on stochastic complementation to derive lower and upper bounds on the equilibrium probability for each state within that set. To show the usefulness of our approach, we present experimental results for several examples from biology. KEY WORDS: Geometric bounds; stochastic complement; Lyapunov function; equilibrium probability distribution; continuous-time Markov chain