  Within the nonparametric diffusion model, we develop a multiple test to infer
about similarity of an unknown drift $b$ to some reference drift $b_0$: At
prescribed significance, we simultaneously identify those regions where
violation from similiarity occurs, without a priori knowledge of their number,
size and location. This test is shown to be minimax-optimal and adaptive. At
the same time, the procedure is robust under small deviation from Brownian
motion as the driving noise process. A detailed investigation for fractional
driving noise, which is neither a semimartingale nor a Markov process, is
provided for Hurst indices close to the Brownian motion case.
