论文标题
对分数Ornstein-uhlenbeck过程的最小二乘估计的改进的浆果界限
An Improved Berry-Esseen Bound of Least Squares Estimation for Fractional Ornstein-Uhlenbeck Processes
论文作者
论文摘要
本文的目的是双重的。首先，它提供了一个新颖的公式来计算Hilbert Space $ \ Mathcal {H} $与Hurst Parameter $ h \ in（0，\ frac12）$相关的有限变化函数的内部产品。该公式基于Lebesgue-Stieljes测量有限变化函数的一种分解以及Lebesgue-Stieljes测量的零件公式的集成。第二，作为公式的应用，我们探讨了作为$ t \ to \ indty $，是双变量函数正常平方的渐近线$ \ MATHCAL {H}^{\ ODOT 2} $（作为$ t $的函数），并改善贝里 - 埃塞恩类型的上限，以最少平方估计分数ornstein-uhlenbeck流程的漂移系数，并使用hurst参数$ h \ in（\ frac14，\ frac14，\ frac12）$。本文的渐近分析比HU，Nualart，Zhou（2019）的引理17的渐近分析要高得多，而改善的浆果 - 埃塞恩型上限是陈的定理1.1结果的最佳改进，李（2021）。作为副产品，给出了上述渐近分析的第二次应用，即，我们还显示了贝里 - 埃塞恩型上限，目的是对分数ornstein-uhlenbeck的漂移系数的矩估计，其中该方法与Sottinen，viititasaaari（2018（2018）中的命题4.1的命题4.1显而易见。
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 $\mathcal{H}$ associated with the fractional Brownian motion with Hurst parameter $H\in (0,\frac12)$. 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 $T\to\infty$, the asymptotic line for the square of the norm of the bivariate function $f_T(t,s)=e^{-θ|t-s|}1_{\{0\leq s,t\leq T\}}$ in the symmetric tensor space $\mathcal{H}^{\odot 2}$ (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 $H\in (\frac14,\frac12)$. 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).
