  We study the problem of parameter estimation for stochastic differential
equations with small noise and fast oscillating parameters. Depending on how
fast the intensity of the noise goes to zero relative to the homogenization
parameter, we consider three different regimes. For each regime, we construct
the maximum likelihood estimator and we study its consistency and asymptotic
normality properties. A simulation study for the first order Langevin equation
with a two scale potential is also provided.
