Product-Form Stationary Distributions for Deficiency Zero Chemical Reaction Networks
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- Anderson, D.F., Craciun, G. & Kurtz, T.G. Bull. Math. Biol. (2010) 72: 1947. doi:10.1007/s11538-010-9517-4
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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.