65th ISI World Statistics Congress 2025 (ISI WSC 2025)

Chemical reaction networks with reaction rates changing stochastically in time

Stochastic Processes and Applications

Since the dawn of stochastic chemical reaction network theory over 50 years ago, there have been many general results about (positive) recurrence, especially in the case of mass-action kinetics. One less-explored area is that of mass-action models whose rate constants, rather than being static, are themselves stochastic. Such models have relevance in applications, since biomolecular systems rarely exist in isolation and their rates often depend on time-changing quantities. In this talk I will introduce the topic and discuss when positive recurrence is achieved in two related settings: the first setting concerns networks with monomolecular complexes whose rates change stochastically over time, based on joint work with Abhishek Pal Majumder and Carsten Wiuf. The second setting concerns models with monomolecular source complexes (but general product complex) and rates randomly switching between two value sets at a low speed, based on joint work with Chuang Xu and Aidan Howells.