  We study the asymptotic behavior of multiscale stochastic spatial gene
networks. Multiscaling takes into account the difference of abundance between
molecules , and captures the dynamic of rare species at a mesoscopic level. We
introduce an assumption of spatial correlations for reactions involving rare
species and a new law of large numbers is obtained. According to the scales,
the whole system splits into two parts with different but coupled dynamics. The
high scale component converges to the usual spatial model which is the solution
of a partial differential equation, whereas, the low scale component converges
to the usual homogeneous model which is the solution of an ordinary
differential equation. Comparisons are made in the supremum norm.
