Tom Kurtz’s work on representation and approximation of stochastic (bio)chemical reaction networks

Abstract

In the 1970s, Tom Kurtz established foundational results on the rigorous approximation of continuous time Markov chains used in modeling chemical reaction networks. These results involved approximation of the stochastic processes over compact time intervals, and included functional laws of large numbers (hydrodynamic/fluid limits), functional central limit theorems (linear noise diffusion approximations), and Langevin-type diffusion approximations (in the strong or pathwise sense). Later on, in the mid 2000s, inspired by the use of biochemical reaction networks as models in systems and synthetic biology, with various collaborators, Tom Kurtz expanded on his earlier results, allowing for multiple time and size scales. This short note summarizes some of Tom Kurtz’s contributions in this arena, which have had an enduring impact on the modeling and analysis of stochastic (bio)chemical reaction networks.