Results on stochastic reaction networks with non-mass action kinetics

2017/12/05 by Anderson, David F., Nguyen, Tung D.
#FOS: Biological sciences #FOS: Mathematics #Probability (math.PR) #Quantitative Methods (q-bio.QM)

paper · doi:10.48550/arxiv.1712.01716

Abstract

In 2010, Anderson, Craciun, and Kurtz showed that if a deterministically modeled reaction network is complex balanced, then the associated stochastic model admits a stationary distribution that is a product of Poissons \citeACK2010. That work spurred a number of followup analyses. In 2015, Anderson, Craciun, Gopalkrishnan, and Wiuf considered a particular scaling limit of the stationary distribution detailed in \citeACK2010, and proved it is a well known Lyapunov function \citeACGW2015. In 2016, Cappelletti and Wiuf showed the converse of the main result in \citeACK2010: if a reaction network with stochastic mass action kinetics admits a stationary distribution that is a product of Poissons, then the deterministic model is complex balanced \citeCW2016. In 2017, Anderson, Koyama, Cappelletti, and Kurtz showed that the mass action models considered in \citeACK2010 are non-explosive (so the stationary distribution characterizes the limiting behavior). In this paper, we generalize each of the three followup results detailed above to the case when the stochastic model has a particular form of non-mass action kinetics.

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