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Product-Form Stationary Distributions for Deficiency Zero Chemical Reaction Networks

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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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Authors and Affiliations

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

    David F. Anderson, Gheorghe Craciun & Thomas G. Kurtz

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  1. David F. Anderson
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  2. Gheorghe Craciun
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  3. Thomas G. Kurtz
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Correspondence to David F. Anderson.

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Anderson, D.F., Craciun, G. & Kurtz, T.G. Product-Form Stationary Distributions for Deficiency Zero Chemical Reaction Networks. Bull. Math. Biol. 72, 1947–1970 (2010). https://doi.org/10.1007/s11538-010-9517-4

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