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, d epending on the relative rates at which the small viscosity parameter and t he homogenization parameter tend to zero. We prove some large-deviations-ty pe estimates, and then apply these results to study wavefronts in both a si ngle reaction-diffusion equation and in a system of reaction-diffusion equa tions. (C) 1999 Published by Elsevier Science B.V. All rights reserved.