Results on stochastic reaction networks with nonmass action kinetics
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 \cite{ACK2010}. 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 \cite{ACK2010}, and proved it is a well known Lyapunov function \cite{ACGW2015}. In 2016, Cappelletti and Wiuf showed the converse of the main result in \cite{ACK2010}: 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 \cite{CW2016}. In 2017, Anderson, Koyama, Cappelletti, and Kurtz showed that the mass action models considered in \cite{ACK2010} are nonexplosive (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 nonmass action kinetics.
 Publication:

arXiv eprints
 Pub Date:
 December 2017
 DOI:
 10.48550/arXiv.1712.01716
 arXiv:
 arXiv:1712.01716
 Bibcode:
 2017arXiv171201716A
 Keywords:

 Mathematics  Probability;
 Quantitative Biology  Quantitative Methods
 EPrint:
 23 pages