Results on stochastic reaction networks with non-mass action kinetics

Results on stochastic reaction networks with non-mass action kinetics

Blog Article

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 [1].That work spurred a number of followup analyses.In 2015, Anderson, Ball - Senior Bottoms Craciun, Gopalkrishnan, and Wiuf considered a particular scaling limit of the stationary distribution detailed in [1], and proved it is a well known Lyapunov function [2].In 2016, Cappelletti and Wiuf showed the converse of the main result in [1]: 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 [3].In 2017, Anderson, Koyama, Cappelletti, and Kurtz showed that the mass action models considered PANTETHINE in [1] 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.