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

Source: [Product-form stationary distributions for deficiency zero chemical reaction networks](<https://www.sota2.com/research/paper/68fa4e981e209131ce95d03a>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-28T13:55:19.213Z

Authors: David F. Anderson, Gheorghe Craciun, Thomas G. Kurtz

Published: 2008-03-20T18:06:39.000Z

## 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.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/0803.3042>)

[PDF](<https://arxiv.org/pdf/0803.3042.pdf>)