 In this paper, we provide the accuracy of the multiscaling model reduction for a stochastic reaction network under a certain multiscaling regime. When a subset of chemical species in a reaction network has much higher abundance than others, the associated stochastic process can be modeled under multiscaling regime. Previous works in the literature showed that the original stochastic system can be approximated with a reduced limiting system, as the scaling parameter N tends to infinity. In general scaling regimes, the convergence to the limiting system can be studied by using the law of large numbers and the relative compactness in a measure space. In this work, by using the Kolmogorov equationwe study the convergence rate of a stochastic network system in the multiscaling nature to a reduce system assuming that each reaction has a constant order propensity. We also provide the convergence of the marginal probability distribution .
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 kinetics and 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 .
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Stochastic models of chemical reaction networks are an important tool to describe and analyze noise effects in cell biology.
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provide the accuracy of the multiscaling model reduction for a stochastic reaction network under a certain multiscaling regime. When a subset of chemical species in a reaction network has much higher abundance than others, the associated stochastic process can be modeled under multiscaling regime. Previous works in the literature showed that the original stochastic system
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
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with a reduced limiting system, as the scaling parameter N tends to infinity. In general scaling regimes,
using an associated reduced system. In this paper, we establish an error bound for this approximation. We consider general chemical kinetics and allow for higher order reactions, which generalizes existing results in the literature. Our approach is based on a direct analysis of
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convergence to the limiting system can be studied by using the law of large numbers and the relative compactness in a measure space. In this work, by using the Kolmogorov equationwe study the convergence rate of a stochastic network system in the multiscaling nature to a reduce system assuming that each reaction has a constant order propensity. We also provide the convergence of the marginal probability distribution
Kolmogorov equation, in contrast to classical approaches in the existing literature