  We study statistical inference for small-noise-perturbed multiscale dynamical
systems where the slow motion is driven by fractional Brownian motion. We
develop statistical estimators for both the Hurst index as well as a vector of
unknown parameters in the model based on a single time series of observations
from the slow process only. We prove that these estimators are both consistent
and asymptotically normal as the amplitude of the perturbation and the
time-scale separation parameter go to zero. Numerical simulations illustrate
the theoretical results.
