Drift estimation for a partially observed mixed fractional Ornstein--Uhlenbeck process
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911361914634240 |
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| author | Cai, Chunhao |
| author_facet | Cai, Chunhao |
| contents | We consider estimation of the drift parameter $\vartheta>0$ in a \emph{partially observed} Ornstein--Uhlenbeck type model driven by a mixed fractional Brownian noise. Our framework extends the partially observed model of \cite{BrousteKleptsyna2010} to the \emph{mixed} case. We construct the canonical innovation representation, derive the associated Kalman filter and Riccati equations, and analyse the asymptotic behaviour of the filtering error covariance.
Within the Ibragimov--Khasminskii LAN framework we prove that the MLE of $\vartheta$, based on continuous observation of the partially observed system on $[0,T]$, is consistent and asymptotically normal with rate $\sqrt{T}$ and the Fisher Information is the same as in \cite{BrousteKleptsyna2010} or the standard Brownian motion case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_15362 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Drift estimation for a partially observed mixed fractional Ornstein--Uhlenbeck process Cai, Chunhao Statistics Theory We consider estimation of the drift parameter $\vartheta>0$ in a \emph{partially observed} Ornstein--Uhlenbeck type model driven by a mixed fractional Brownian noise. Our framework extends the partially observed model of \cite{BrousteKleptsyna2010} to the \emph{mixed} case. We construct the canonical innovation representation, derive the associated Kalman filter and Riccati equations, and analyse the asymptotic behaviour of the filtering error covariance. Within the Ibragimov--Khasminskii LAN framework we prove that the MLE of $\vartheta$, based on continuous observation of the partially observed system on $[0,T]$, is consistent and asymptotically normal with rate $\sqrt{T}$ and the Fisher Information is the same as in \cite{BrousteKleptsyna2010} or the standard Brownian motion case. |
| title | Drift estimation for a partially observed mixed fractional Ornstein--Uhlenbeck process |
| topic | Statistics Theory |
| url | https://arxiv.org/abs/2512.15362 |