Mixed sub-fractional Brownian motion and drift estimation of related Ornstein-Uhlenbeck process

In this paper, we will first use the fundamental martingale of the mixed sub-fractional Brownian motion to construct the Skorohod integral and study the relationship between the Skorohod integral and forward path-wise integral when the Hurst parameter $H>1/2$. Based on their relationship, we propose the least squares estimator for the mixed sub-fractional Ornstein-Uhlenbeck process with a continuous record of observations. To overcome the difficulty of simulation, we will simulate the sub-fractional Brownian motion in the sense of strong convergence for the first time and introduce a practical estimator associated with the LSE