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