标题： 缓和分数布朗运动的测试 显示英文标题

标题： Testing of tempered fractional Brownian motions

摘要： 我们提出了一种基于自协方差、去趋势移动平均以及时间平均均方位移统计量的测试方法，用于研究与半长程相关性和瞬态反常扩散相关的 tempered 分数布朗运动（TFBMs）。 在此框架下，我们考虑了三种类型的 TFBMs：两种在其移动平均表示中加入了温控因子，另一种在其自相关公式中加入了温控参数。 我们利用分位数线来展示它们的动力学行为。 通过所提出的测试方法，我们对这些测试进行了全面的势分析。结果显示，这些测试能够区分具有不同 Hurst 参数的温控过程。 显示英文摘要

摘要： We propose here a testing methodology based on the autocovariance, detrended moving average, and time-averaged mean-squared displacement statistics for tempered fractional Brownian motions (TFBMs) which are related to the notions of semi-long range dependence and transient anomalous diffusion. In this framework, we consider three types of TFBMs: two with a tempering factor incorporated into their moving-average representation, and one with a tempering parameter added to the autocorrelation formula. We illustrate their dynamics with the use of quantile lines. Using the proposed methodology, we provide a comprehensive power analysis of the tests. It appears that the tests allow distinguishing between the tempered processes with different Hurst parameters.