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Bull Math Biol. 2010 Nov;72(8):1947-70. doi: 10.1007/s11538-010-9517-4. Epub 2010 Mar 20.

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

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Department of Mathematics, University of Wisconsin, Madison, WI 53706, USA.


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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