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Stochastic computational models in the form of pure jump processes occurfrequently in the description of chemical reactive processes, of ion channeldynamics, and of the spread of infections in populations. For spatiallyextended models, the computational complexity can be rather high such thatapproximate multiscale models are attractive alternatives. Within thisframework some variables are described stochastically, while others areapproximated with a macroscopic point value.  We devise theoretical tools for analyzing the pathwise multiscale convergenceof this type of variable splitting methods, aiming specifically at spatiallyextended models. Notably, the conditions we develop guarantee well-posedness ofthe approximations without requiring explicit assumptions of \textit{a priori}bounded solutions. We are also able to quantify the effect of the differentsources of errors, namely the \emph{multiscale error} and the \emph{splittingerror}, respectively, by developing suitable error bounds. Computationalexperiments on selected problems serve to illustrate our findings.

Pathwise error bounds in Multiscale variable splitting methods for spatial stochastic kinetics