{"ID":2828010,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.15362","arxiv_id":"2512.15362","title":"Drift estimation for a partially observed mixed fractional Ornstein--Uhlenbeck process","abstract":"We consider estimation of the drift parameter $\\vartheta\u003e0$ 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.","short_abstract":"We consider estimation of the drift parameter $\\vartheta\u003e0$ 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 represe...","url_abs":"https://arxiv.org/abs/2512.15362","url_pdf":"https://arxiv.org/pdf/2512.15362v2","authors":"[\"Chunhao Cai\"]","published":"2025-12-17T12:06:54Z","proceeding":"math.ST","tasks":"[\"math.ST\"]","methods":"[]","has_code":false}