Stochastic models of chemical reaction networks are an important tool to describe and analyze noise effects in cell biology. In this paper, we consider a particular multiscaling limit for a class of stochastic reaction systems, with the property that all reactions initially take place at an approximately constant rate . It is known that the model can be approximated using an associated reduced system . In this paper, we  establish an error bound for this approximation. We consider general chemical kineticsand allow for higher order reactions , 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.
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.
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In this paper, we consider a particular multiscaling limit for a class of stochastic reaction systems, with the property that all reactions initially take place at an approximately constant rate
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
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the model
multiscale models
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using an associated reduced system
with a reduced system such as mean field dynamics or hybrid systems, but the accuracy of the approximation remains unknown
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estimate the probability distribution of low copy species in multiscale stochastic reaction systems under short-time scale. We also
R
We consider general chemical kineticsand allow for higher order reactions
Throughout the manuscript, typical mass action systems are mainly handled, but we also show that the main theorem can extended to general kinetics