Product-form stationary distributions for deficiency zero chemical reaction networks

Details Product-form stationary distributions for deficiency zero chemical reaction networks Product-form stationary distributions for deficiency zero chemical reaction networks

2008-03-20

arxiv.org/abs/0803.3042v4

Mathematics

Probability

Final changes. Added an example demonstrating usefulness of main result in multi-scale setting

Scientific paper

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.

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