Bounding the equilibrium distribution of Markov population models

Abstract

SUMMARY 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. Copyright © 2011 John Wiley & Sons, Ltd.