2023/09/19 by Yong Chen, Ying Li, Chen, Yong +1
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #Advanced Statistical Methods and Models #Advanced Statistical Process Monitoring #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR)
paper · pdf · doi:10.48550/arxiv.2309.10415
openalex publication_date 2023/09/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The process (Gt)t∈[0,T] is referred to as a fractional Gaussian process if the first-order partial derivative of the difference between its covariance function and that of the fractional Brownian motion (BHt)t∈[0,T ] is a normalized bounded variation function. We quantify the relation between the associated reproducing kernel Hilbert space of (G) and that of (BH). Seven types of Gaussian processes with non-stationary increments in the literature belong to it. In the context of applications, we demonstrate that the Gladyshev's theorem holds for this process, and we provide Berry-Esséen upper bounds associated with the statistical estimations of the ergodic fractional Ornstein-Uhlenbeck process driven by it. The second application partially builds upon the idea introduced in \citeBBES 23, where they assume that (G) has stationary increments. Additionally, we briefly discuss a variant of this process where the covariance structure is not entirely linked to that of the fractional Brownian motion.