Bounding the equilibrium distribution of Markov population models
Date
2011-10-18
Authors
Dayar T.
Hermanns, H.
Spieler, D.
Wolf, V.
Editor(s)
Advisor
Supervisor
Co-Advisor
Co-Supervisor
Instructor
Source Title
Numerical Linear Algebra with Applications
Print ISSN
1099-1506
Electronic ISSN
Publisher
Wiley-Blackwell Publishing Ltd.
Volume
18
Issue
6
Pages
931 - 946
Language
English
Type
Journal Title
Journal ISSN
Volume Title
Series
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. Copyright © 2011 John Wiley & Sons, Ltd.