Convergence rate of CLT for the drift estimation of sub-fractional Ornstein–Uhlenbeck process of second kind
In this paper, we deal with an Ornstein–Uhlenbeck process driven by sub-fractional Brownian motion of the second kind with Hurst index $H\in (\frac{1}{2},1)$. We provide a least squares estimator (LSE) of the drift parameter based on continuous-time observations. The strong consistency and the upper...
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| Format: | Article |
| Language: | English |
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VTeX
2021-05-01
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| Series: | Modern Stochastics: Theory and Applications |
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| Online Access: | https://www.vmsta.org/doi/10.15559/21-VMSTA179 |
| _version_ | 1818365675401379840 |
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| author | Maoudo Faramba Baldé Khalifa Es-Sebaiy |
| author_facet | Maoudo Faramba Baldé Khalifa Es-Sebaiy |
| author_sort | Maoudo Faramba Baldé |
| collection | DOAJ |
| description | In this paper, we deal with an Ornstein–Uhlenbeck process driven by sub-fractional Brownian motion of the second kind with Hurst index $H\in (\frac{1}{2},1)$. We provide a least squares estimator (LSE) of the drift parameter based on continuous-time observations. The strong consistency and the upper bound $O(1/\sqrt{n})$ in Kolmogorov distance for central limit theorem of the LSE are obtained. We use a Malliavin–Stein approach for normal approximations. |
| first_indexed | 2024-12-13T22:24:02Z |
| format | Article |
| id | doaj.art-d678151dbcc3446f9161c4345cc89cdb |
| institution | Directory Open Access Journal |
| issn | 2351-6046 2351-6054 |
| language | English |
| last_indexed | 2024-12-13T22:24:02Z |
| publishDate | 2021-05-01 |
| publisher | VTeX |
| record_format | Article |
| series | Modern Stochastics: Theory and Applications |
| spelling | doaj.art-d678151dbcc3446f9161c4345cc89cdb2022-12-21T23:29:17ZengVTeXModern Stochastics: Theory and Applications2351-60462351-60542021-05-018332934710.15559/21-VMSTA179Convergence rate of CLT for the drift estimation of sub-fractional Ornstein–Uhlenbeck process of second kindMaoudo Faramba Baldé0Khalifa Es-Sebaiy1Cheikh Anta Diop University, Dakar, SenegalDepartment of Mathematics, Faculty of Science, Kuwait University, KuwaitIn this paper, we deal with an Ornstein–Uhlenbeck process driven by sub-fractional Brownian motion of the second kind with Hurst index $H\in (\frac{1}{2},1)$. We provide a least squares estimator (LSE) of the drift parameter based on continuous-time observations. The strong consistency and the upper bound $O(1/\sqrt{n})$ in Kolmogorov distance for central limit theorem of the LSE are obtained. We use a Malliavin–Stein approach for normal approximations.https://www.vmsta.org/doi/10.15559/21-VMSTA179Sub-fractional Ornstein–Uhlenbeck process of second kindleast squares estimatorBerry–Esséen boundMalliavin–Stein approach for normal approximations |
| spellingShingle | Maoudo Faramba Baldé Khalifa Es-Sebaiy Convergence rate of CLT for the drift estimation of sub-fractional Ornstein–Uhlenbeck process of second kind Modern Stochastics: Theory and Applications Sub-fractional Ornstein–Uhlenbeck process of second kind least squares estimator Berry–Esséen bound Malliavin–Stein approach for normal approximations |
| title | Convergence rate of CLT for the drift estimation of sub-fractional Ornstein–Uhlenbeck process of second kind |
| title_full | Convergence rate of CLT for the drift estimation of sub-fractional Ornstein–Uhlenbeck process of second kind |
| title_fullStr | Convergence rate of CLT for the drift estimation of sub-fractional Ornstein–Uhlenbeck process of second kind |
| title_full_unstemmed | Convergence rate of CLT for the drift estimation of sub-fractional Ornstein–Uhlenbeck process of second kind |
| title_short | Convergence rate of CLT for the drift estimation of sub-fractional Ornstein–Uhlenbeck process of second kind |
| title_sort | convergence rate of clt for the drift estimation of sub fractional ornstein uhlenbeck process of second kind |
| topic | Sub-fractional Ornstein–Uhlenbeck process of second kind least squares estimator Berry–Esséen bound Malliavin–Stein approach for normal approximations |
| url | https://www.vmsta.org/doi/10.15559/21-VMSTA179 |
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