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We investigate the asymptotic properties of Markov processes associated tostochastic chemical reaction networks (CRNs) driven by the kinetics of the lawof mass action. Their transition rates exhibit a polynomial dependence on thestate variable, with possible discontinuities of the dynamics along theboundary of the state space. As a natural choice to study stability propertiesof CRNs, the scaling parameter considered in this paper is the norm of theinitial state. Compared to existing scalings of the literature, this scalingdoes not change neither the topology of a CRN, nor its reactions constants.Functional limit theorems with this scaling parameter can be used to provepositive recurrence of the Markov process. This scaling approach also givesinteresting insights on the transient behavior of these networks, to describehow multiple time scales drive the time evolution of their sample paths forexample. General stability criteria are presented as well as a possibleframework for scaling analyses. Several simple examples of CRNs areinvestigated with this approach. A detailed stability and scaling analyses of aCRN with slow and fast timescales is worked out.

A Scaling Approach to Stochastic Chemical Reaction Networks