Before revision:  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 .
After revision:  In general scaling regimes, the Kolmogorov equation, in contrast to classical approaches in the existing literature .