Bulletin of Mathematical Biology

, Volume 72, Issue 8, pp 1947–1970 | Cite as

Product-Form Stationary Distributions for Deficiency Zero Chemical Reaction Networks

  • David F. Anderson
  • Gheorghe Craciun
  • Thomas G. Kurtz
Original Article

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.

Keywords

Product-form stationary distributions Deficiency zero 

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Copyright information

© Society for Mathematical Biology 2010

Authors and Affiliations

  • David F. Anderson
    • 1
  • Gheorghe Craciun
    • 1
  • Thomas G. Kurtz
    • 1
  1. 1.Department of MathematicsUniversity of WisconsinMadisonUSA

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