Drift estimation for a partially observed mixed fractional Ornstein--Uhlenbeck process

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.