14th European Conference on Mathematical and Theoretical Biology (ECMTB 2026)

Stochastic Reaction Networks: Definition, Classical Scaling and Long-Term Behavior

Past, Present, and Future of Reaction Networks Theory

Stochastic reaction networks, modelled as continuous-time Markov chains, provide a principled framework for capturing the inherent randomness in biochemical and population systems. In this overview, I will introduce them and present the classical scaling limit, which establishes convergence to the deterministic reaction network model on compact time intervals as the system size grows. A natural question then arises: does this approximation persist over long-time horizons? The study of limit distributions is motivated both by the analysis of biological models over long-time intervals and by multiscale models, where fast subsystems are approximated by their stationary regime. I will discuss notable connections and discrepancies between the stochastic and deterministic long-term dynamics, highlighting the case of complex-balanced models. Time permitting, I will close with some related open problems.