A comparison of homogenization and large deviations, with applications to wavefront propagation

We consider the combined effects of homogenization and large deviations in a stochastic differential equation. We show that there are three regimes, depending on the relative rates at which the small viscosity parameter and the homogenization parameter tend to zero. We prove some large-deviations-type estimates, and then apply these results to study wavefronts in both a single reaction–diffusion equation and in a system of reaction–diffusion equations.