报告题目：Random Ratios concerning to Complex Fractional Ornstein-Uhlenbeck Processes with Hurst parameter H ∈(0, 1/2) and others

报告时间：2024-05-25  09:00-10:00

报 告 人：陈勇 副教授 (江西师范大学）

报告地点：理学院西北楼103

Abstract: We study the strong consistency and asymptotic normality of a least squares estimator of the drift coefficient for complex-valued Ornstein-Uhlenbeckprocesses driven by fractional noise, extending the results of Chen, Hu, Wang (2017) to fractional noise with Hurst parameter H ∈ (1/4, 1/2) and the results of Hu, Nualart, Zhou (2019) to a two-dimensional case. When H ∈ (0, 1/4], it is found that the integrand functions of the estimator are not in the domain of the standard divergence operator. The paper also develops a new and simplified inner formula of the fractional Brownian motion with Hurst parameter H ∈ (0, 1/2), and this new formula is then applied to obtain the second moments of the so-called α-order fractional Brownian motion and the α-fractional bridges when the Hurst parameter H ∈ (0, 1/2). Joint work with Fares ALAZEMIa,AbdulazizALSENAFI, and HongjuanZHOU.