论文标题
标量厄贡扩散的尖锐自适应和路径稳定的相似性测试
Sharp adaptive and pathwise stable similarity testing for scalar ergodic diffusions
论文作者
论文摘要
在非参数扩散模型中，我们开发了一项多次测试，以推断出未知漂移$ b $与某些参考漂移$ b_0 $的相似性：以规定的意义，我们同时确定了发生违反相似性的区域，而无需先验地了解其数量，大小和位置。该测试被证明是最小的和自适应的。同时，在与布朗运动作为驾驶噪声过程的小偏差下，该过程是牢固的。对于靠近布朗尼运动案例的赫斯特指数，提供了针对分数驾驶噪声的详细研究，它既不是半司机也不是马尔可夫的过程。
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.
