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arXiv · 2406.18004

Parameter Estimation for the Complex Fractional Ornstein-Uhlenbeck Processes with Hurst parameter H \in (0, 1/2)

Fares Alazemi·Abdulaziz Alsenafi·Yong Chen·Hongjuan Zhou
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Abstract

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 Chen, Hu, Wang (2017) to the case of Hurst parameter H \in (1/4 , 1/2) and the results of Hu, Nualart, Zhou (2019) to a two-dimensional case. When H \in (0, 1/4], 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, 1/2). 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, 1/2).

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Fares Alazemi, Abdulaziz Alsenafi, Yong Chen, Hongjuan Zhou. 2024-06-26. Parameter Estimation for the Complex Fractional Ornstein-Uhlenbeck Processes with Hurst parameter H \in (0, 1/2). https://arxiv.org/abs/2406.18004

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