We consider the impact of noise on the stability and propagation
of fronts in an excitable media with a piece-wise smooth, discontinuous ignition
process. In a neighborhood of the ignition threshold the system interacts strongly with noise, the front can
loose monotonicity, resulting in multiple crossings of the ignition threshold.
We adapt the renormalization group methods developed for coherent structure
interaction, a key step being to determine pairs of function spaces for which the
the ignition function is Frechet differentiable, but for which the
associated semi-group, $S(t)$, is integrable at $t=0$.
We parameterize a neighborhood of the front solution through a dynamic front position and
a co-dimension one remainder. The front evolution and the asymptotic decay
of the remainder are on the same time scale, the RG approach shows that the
remainder becomes asymptotically small, in terms of the noise strength and regularity, and the front
propagation is driven by a competition between the ignition process and the noise.