2022/10/02 by Yong Chen, Chen, Yong, Xiangmeng Gu +1
Economics, Econometrics and Finance · Mathematics · #60G15 #60G22 #62M09 #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Statistical Methods and Inference #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2210.00420
openalex publication_date 2022/10/02 · openalex created_date 2022/10/06 · openalex updated_date 2026/07/28
The aim of this paper is twofold. First, it offers a novel formula to calculate the inner product of the bounded variation function in the Hilbert space H associated with the fractional Brownian motion with Hurst parameter H∈ (0,\frac12). This formula is based on a kind of decomposition of the Lebesgue-Stieljes measure of the bounded variation function and the integration by parts formula of the Lebesgue-Stieljes measure. Second, as an application of the formula, we explore that as T→∞, the asymptotic line for the square of the norm of the bivariate function fT(t,s)=e-θ|t-s|1_\0≤ s,t≤ T\ in the symmetric tensor space H\odot 2 (as a function of T), and improve the Berry-Esséen type upper bound for the least squares estimation of the drift coefficient of the fractional Ornstein-Uhlenbeck processes with Hurst parameter H∈ (\frac14,\frac12). The asymptotic analysis of the present paper is much more subtle than that of Lemma 17 in Hu, Nualart, Zhou(2019) and the improved Berry-Esséen type upper bound is the best improvement of the result of Theorem 1.1 in Chen, Li (2021). As a by-product, a second application of the above asymptotic analysis is given, i.e., we also show the Berry-Esséen type upper bound for the moment estimation of the drift coefficient of the fractional Ornstein-Uhlenbeck processes where the method is obvious different to that of Proposition 4.1 in Sottinen, Viitasaari(2018).