Department of Mathematics, University of Wisconsin, Madison, WI 53706, USA.
Bull Math Biol. 2010 Nov;72(8):1947-70. doi: 10.1007/s11538-010-9517-4. Epub 2010 Mar 20.
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.
我们考虑具有质量作用动力学的随机模型化化学反应系统，并证明如果具有质量作用动力学的类似确定性模型系统存在复杂平衡平衡，则对于状态空间的每个封闭的、不可约子集都存在乘积形式的固定分布。然后，费因伯格的零缺陷定理意味着只要相应的化学网络是弱可逆的且具有零缺陷，就存在这样的分布。随机模型化系统的固定分布的主要参数是相应确定性模型化系统的复杂平衡平衡值。我们还将我们的主要结果推广到一些非质量作用动力学。
