LAN Property for the Drift and Hurst Paramters in The Mixed Fractional O-U Process with Continuous Observations

Abstract: This paper deals with the Local Asymptotical normality for the joint drift parameter and Hurst parameter $H>3/4$ in the mixed fractional Ornstein-Uhlenbeck process. Different from the only estimation of the drift parameter when $H$ is known, we will use the fact that the mixed fractional Brownian motion is a semimartingale with its own filtering when $H>3/4$.