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.

翻译：在非参数扩散模型框架下，我们发展了一种多重检验方法，用于推断未知漂移函数$b$与参考漂移函数$b_0$的相似性：在预设显著性水平下，该方法无需预先知道违反相似性区域的数量、大小和位置，即可同时识别这些区域。该检验被证明具有极小化最优性和自适应性。同时，当驱动噪声过程存在对布朗运动的小偏差时，该程序仍具有稳健性。针对分数阶驱动噪声（既非半鞅也非马尔可夫过程），我们在赫斯特指数接近布朗运动情形下提供了详细分析。