The Relationship between Stochastic and Deterministic Models for Chemical Reactions

TLDR

The Markov chain and ordinary differential equation models for chemical reaction systems are compared. The study demonstrates that, when the reaction volume is properly incorporated into the Markov chain formulation, the ODE model emerges as its infinite‑volume limit, and a central limit theorem quantifies the deviation between the two models.

Abstract

The Markov chain and ordinary differential equation models for chemical reaction systems are compared. It is shown that if the volume of the reaction system is taken into account in an appropriate way in the formulation of the Markov chain model, then the o.d.e. model is the infinite volume limit of the Markov chain model. A central limit theorem is also given for the deviation of the Markov chain model from the o.d.e. model.