We study statistical inference for small-noise-perturbed multiscale dynamical systems where the slow motion is driven by fractional Brownian motion. We develop statistical estimators for both the Hurst index as well as a vector of unknown parameters in the model based on a single time series of observations from the slow process only. We prove that these estimators are both consistent and asymptotically normal as the amplitude of the perturbation and the time-scale separation parameter go to zero. Numerical simulations illustrate the theoretical results.

翻译：我们研究小噪音隔音多尺度动态系统的统计推论,缓慢运动是由分形布朗运动驱动的。我们为赫斯特指数和模型中未知参数的矢量开发统计估计器,这些参数的矢量以单一时间序列的慢过程观测结果为基础。我们证明这些估计器在扰动和时间尺度分离参数的振幅变为零时,是一致和无干扰的正常。数字模拟显示了理论结果。