# Results on stochastic reaction networks with non-mass action kinetics Source: [Results on stochastic reaction networks with non-mass action kinetics]() Collection index: [llms.txt]() Data updated: 2025-10-25T13:00:31.146Z Authors: David F. Anderson, Tung D. Nguyen Published: 2017-12-05T15:46:47.000Z ## 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 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. ## Recorded benchmark results A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage. ## Original sources and implementation [Original paper]() [PDF]()