  We formulate the large deviations for a class of two scale chemical kinetic
processes motivated from biological applications. The result is successfully
applied to treat a genetic switching model with positive feedbacks. The
corresponding Hamiltonian is convex with respect to the momentum variable as a
by-product of the large deviation theory. This property ensures its superiority
in the rare event simulations compared with the result obtained by formal WKB
asymptotics. The result is of general interest to understand the large
deviations for multiscale problems.
