  We study statistical inference for small-noise-perturbed multiscale dynamical
systems. We prove consistency, asymptotic normality, and convergence of all
scaled moments of an appropriately-constructed maximum likelihood estimator
(MLE) for a parameter of interest, identifying precisely its limiting variance.
We allow full dependence of coefficients on both slow and fast processes, which
take values in the full Euclidean space; coefficients in the equation for the
slow process need not be bounded and there is no assumption of periodic
dependence. The results provide a theoretical basis for calibration of
small-noise-perturbed multiscale dynamical systems. Data from numerical
simulations are presented to illustrate the theory.
