Parameter Estimation for the Complex Fractional Ornstein-Uhlenbeck Processes with Hurst parameter H \in (0, 1/2)
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866910502223872000 |
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| author | Alazemi, Fares Alsenafi, Abdulaziz Chen, Yong Zhou, Hongjuan |
| author_facet | Alazemi, Fares Alsenafi, Abdulaziz Chen, Yong Zhou, Hongjuan |
| contents | 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 α-order fractional Brownian motion and the α-fractional bridges with the Hurst parameter H \in (0, 1/2). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_18004 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Parameter Estimation for the Complex Fractional Ornstein-Uhlenbeck Processes with Hurst parameter H \in (0, 1/2) Alazemi, Fares Alsenafi, Abdulaziz Chen, Yong Zhou, Hongjuan Probability 60G15, 60G22, 62M09 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 α-order fractional Brownian motion and the α-fractional bridges with the Hurst parameter H \in (0, 1/2). |
| title | Parameter Estimation for the Complex Fractional Ornstein-Uhlenbeck Processes with Hurst parameter H \in (0, 1/2) |
| topic | Probability 60G15, 60G22, 62M09 |
| url | https://arxiv.org/abs/2406.18004 |