Product-form stationary distributions for deficiency zero chemical reaction networks
Abstract
We consider stochastically modeled chemical reaction systems with mass-action kinetics and prove that a product-form stationary distribution exists for each closed, irreducible subset of the state space if an analogous deterministically modeled system with mass-action kinetics admits a complex balanced equilibrium. Feinberg's deficiency zero theorem then implies that such a distribution exists so long as the corresponding chemical network is weakly reversible and has a deficiency of zero. The main parameter of the stationary distribution for the stochastically modeled system is a complex balanced equilibrium value for the corresponding deterministically modeled system. We also generalize our main result to some non-mass-action kinetics.
Keywords
Cite
@article{arxiv.0803.3042,
title = {Product-form stationary distributions for deficiency zero chemical reaction networks},
author = {David F. Anderson and Gheorghe Craciun and Thomas G. Kurtz},
journal= {arXiv preprint arXiv:0803.3042},
year = {2010}
}
Comments
Final changes. Added an example demonstrating usefulness of main result in multi-scale setting