题  目：Parameter Estimation for the Complex Fractional Ornstein-Uhlenbeck Processes with Hurst parameter $H \in (0,0 \frac12)$

主讲人：陈勇 教授

时  间：2025年6月4日14:30

地  点：段家滩校区贵和楼505

主讲人简介：

陈勇，副教授，硕士生导师，保山学院大数据学院学术副院长。本科毕业于中国海洋大学（1998），硕士及博士毕业于北京大学（2001，2006），曾国家公派访问美国堪萨斯大学数学系。主要从事随机过程，随机分析及其应用的研究工作。在 Stoch. Process Their Appl. ，Journal of theoretical probability，Journal of Applied Probability，Journal of Statistical Planning and Inference，Journal of Mathematical Physics，Chaos Solitons  Fractals，Kyoto Journal of Mathematics，Infin. Dimens. Anal. Quantum. Probab. Relat. Top.，ALEA Lat. Am. J. Probab. Math. Stat. 等数学和概率统计主流期刊上发表学术论文36篇。主持国家自然科学基金青年基金一项（2012-2014），地区基金两项（2020-2023，2025-2028）。

报告内容：

We study the strong consistency and asymptotic normality of a least squares estimator of the drift coefficient in complex-valued Ornstein-Uhlenbeck processes driven by fractional Brownian motion, extending  the results  of \cite{chw} to the case of Hurst parameter $H\in (\frac14,\frac12)$ and the results of \cite{hnz 19} to a two-dimensional case. When $H\in (0,\frac14]$,  it is found that the integrand of the estimator is not in the domain of the standard divergence operator. To facilitate the proofs, we develop a new inner product formula for functions of bounded variation in the reproducing kernel Hilbert space of fractional Brownian motion with Hurst parameter $H\in (0,\frac12)$. This formula is also applied to obtain the second moments of the so-called $\alpha$-order fractional Brownian motion and the $\alpha$-fractional bridges with the Hurst parameter $H\in (0,\frac12)$.