  Stochastic models of chemical reaction networks are an important tool to
describe and analyze noise effects in cell biology. When chemical species and
reaction rates in a reaction system have different orders of magnitude, the
associated stochastic system is often modeled in a multiscale regime. It is
known that multiscale models can be approximated with a reduced system such as
mean field dynamics or hybrid systems, but the accuracy of the approximation
remains unknown. In this paper, we estimate the probability distribution of low
copy species in multiscale stochastic reaction systems under short-time scale.
We also establish an error bound for this approximation. Throughout the
manuscript, typical mass action systems are mainly handled, but we also show
that the main theorem can extended to general kinetics, which generalizes
existing results in the literature. Our approach is based on a direct analysis
of the Kolmogorov equation, in contrast to classical approaches in the existing
literature.
