  In a stochastic reaction network setting we consider the problem of tracking
the fate of individual molecules. We show that using the classical large volume
limit results, we may approximate the dynamics of a single tracked molecule in
a simple and computationally efficient way. We give examples on how this
approach may be used to obtain various characteristics of single-molecule
dynamics (for instance, the distribution of the number of infections in a
single individual in the course of an epidemic or the activity time of a single
enzyme molecule). Moreover, we show how to approximate the overall dynamics of
species of interest in the full system with a collection of independent
single-molecule trajectories, and give explicit bounds for the approximation
error in terms of the reaction rates. This approximation, which is well defined
for all times, leads to an efficient and fully parallelizable simulation
technique for which we provide some numerical examples.
