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，我们开发了一种多重检验方法，用于推断未知漂移项$b$与参考漂移项$b_0$之间的相似性：在指定显著性水平下，该方法能同时识别出违背相似性的区域，且无需预先知道这些区域的数量、大小和位置。该检验被证明具有极小化最优性和自适应性。同时，该过程在驱动噪声过程偏离布朗运动较小的情形下具有稳健性。针对驱动噪声为分数布朗运动（既非半鞅也非马尔可夫过程）的情形，本文在赫斯特指数接近布朗运动情形时进行了详细研究。