  We consider the classical estimation problem of an unknown drift parameter
within classes of nondegenerate diffusion processes. Using rough path theory
(in the sense of T. Lyons), we analyze the Maximum Likelihood Estimator (MLE)
with regard to its pathwise stability properties as well as robustness toward
misspecification in volatility and even the very nature of the noise. Two
numerical examples demonstrate the practical relevance of our results.
